essays in financial economics - cmu

DISSERTATION

Essays in Financial Economics

Presented by

EMILIO BISETTI

Submitted to the Tepper School of Business

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

at

CARNEGIE MELLON UNIVERSITY

April 2018

Dissertation Committee:

Burton Hollifield (Co-Chair)

Stephen A. Karolyi

Stefan Lewellen

Pierre Jinghong Liang

Chris Telmer

Ariel Zetlin-Jones (Co-Chair)

c© Emilio Bisetti 2018ALL RIGHTS RESERVED

Acknowledgments

I am deeply indebted to Burton Hollifield, Ariel Zetlin-Jones, and Chris Telmer, for their endlesssupport and guidance throughout the years. They taught me much of what I know about research,economics, and finance. They spent countless hours listening to, discussing, and helping me de-velop my research ideas. They always treated me as a colleague and a friend, and never stoppedencouraging me to do better.

I am extremely grateful to Steve Karolyi and Stefan Lewellen for their invaluable energy and support.The first chapter of this dissertation greatly improved in quality and depth thanks to their selflesshelp, and they have been fantastic mentors during my job market.

I thank Laurence Ales and Finn Kydland for organizing Macro-Finance PhD workshops and stimu-lating a collaborative research environment between Tepper PhD students. I am also grateful to themany Tepper faculty who generously offered their time to provide feedback to my work. I am parti-cularly grateful to Pierre Liang for serving in my dissertation committee.

I thank my friends and fellow PhD students for years of intense work and fun. In particular, I thankHakkı Ozdenoren, Alex Schiller, and Ben Tengelsen, for endless conversations about economics andfinance. Both the content of my research and my ability to communicate my research to others havegreatly benefited from these conversations. I am especially grateful to Lawrence Rapp and Laila Leefor their invaluable assistance with administrative matters.

I consider myself lucky for having such wonderful friends outside of work as Giorgio Antongio-vanni; Alessandro Biggi; Francesco Brachetti; Ciprian Domnisoru; Daniela Frattini; Christian Frem;Maria Pia Guffanti; Francesco Maccarana; Fulvio Mazza; Andrea Mazzanti; Giacomo Meo; FrancescoMorandi; Marie-Lou and Dana Nahhas; Fares Nimri; Nicola Paccanelli; Pietro Pollichieni; CristinaSangaletti; Andrea Tremaglia; and Dario Zocchi. Their friendship has been essential for me to succeedin graduate school.

Finally, I am truly grateful to Jana for her love and for her patient support during the last years ofmy doctorate. My biggest thanks goes to family for listening to, understanding, and supporting meat every step of my life. This dissertation is dedicated to them.

i

A Silvia, Paolo,Alberto, e Francesco.

Abstract

In the first essay, I address the current debate on the costs and benefits of financial regulation, andI show that financial regulation can increase bank shareholder value by reducing shareholder moni-toring costs. I use a regression discontinuity design to study the effect of an unexpected decrease insmall-bank reporting requirements to the Federal Reserve. Using the reporting change as a negativeshock to regulatory monitoring by the Fed, I find that reduced Fed monitoring leads to a 1% lossin Tobin’s q and a 7% loss in equity market-to-book. I show that these losses come from increasedinternal monitoring expenditures, managerial rents, and monitoring conflicts between shareholders.My results are among the first to quantify the shareholder value of monitoring.

In the second essay (with Benjamin Tengelsen and Ariel Zetlin-Jones), we re-examine the importanceof separation between ownership and labor in team production models that feature free riding. Insuch models, conventional wisdom suggests an outsider is needed to administer incentive schemesthat do not balance the budget. We analyze the ability of insiders to administer such incentive sche-mes in a repeated team production model with free riding when they lack commitment. Specifically,we augment a standard, repeated team production model by endowing insiders with the ability toimpose group punishments which occur after team outcomes are observed but before the subsequentround of production. We extend techniques from Abreu (1986) to characterize the entire set of perfect-public equilibrium payoffs and find that insiders are capable of enforcing welfare enhancing grouppunishments when they are sufficiently patient.

In the third essay, I re-examine an important prediction of asset pricing theory which has historicallyfound little support in the data—that expected consumption growth and equity returns should becorrelated. I first show empirically that advertising growth is a good proxy for expected consumptiongrowth, as it predicts both consumption growth and equity returns in aggregate post-war US data.To shed light on the link between advertising growth, expected consumption, and expected returns, Ithen build and calibrate a dynamic model of goods market frictions where firms invest in advertisingto build their customer capital (as in Gourio and Rudanko (2014)). Within the model, I show that theseverity of goods market frictions is a key element to replicate the predictability patterns I observe inthe data.

iii

Contents

Acknowledgments i

Abstract iii

1 The Value of Regulators as Monitors: Evidence from Banking 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Institutional Background and Motivating Theory . . . . . . . . . . . . . . . . . . . . . . 6

1.2.1 Institutional Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.2 Predictions from Agency Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 Empirical Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.3.1 Data Sources and Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.3.2 Estimation Strategy and Identification . . . . . . . . . . . . . . . . . . . . . . . . 15

1.4 The Value of Regulatory Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.4.1 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.4.2 Robustness, Placebo, and Falsification Tests . . . . . . . . . . . . . . . . . . . . . 21

1.5 How does Regulatory Monitoring Benefit Shareholders? . . . . . . . . . . . . . . . . . 23

1.5.1 Bank Value, Monitoring Expenditure, and Managerial Rents . . . . . . . . . . . 23

1.5.2 Regulatory Monitoring and Shareholder Free-Riding . . . . . . . . . . . . . . . 30

1.6 Discussion and Tests of Alternative Hypotheses . . . . . . . . . . . . . . . . . . . . . . 32

1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

v

vi CONTENTS

2 Group Punishments without Commitment 37

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.2 A Generalized Model of Repeated Team Production . . . . . . . . . . . . . . . . . . . . 42

2.2.1 Stage Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.2.2 Infinitely-Repeated Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.3 An Application: Repeated Oligopoly with a Principal . . . . . . . . . . . . . . . . . . . 57

2.3.1 Stage Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

2.3.2 Infinitely-Repeated Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

2.3.3 Substitutability and Price Externalities . . . . . . . . . . . . . . . . . . . . . . . 62

2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3 Advertising, Consumption, and Asset Prices 67

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.2 Aggregate Advertising Expenditures and Equity Returns . . . . . . . . . . . . . . . . . 71

3.2.1 Consumption Growth and Excess Returns Predictability . . . . . . . . . . . . . 72

3.2.2 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

3.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

3.3.1 Firm Problem and Return on Equity . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.3.2 Household Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.3.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.4.1 Calibration and Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.4.2 Simulated Moments and Predictability . . . . . . . . . . . . . . . . . . . . . . . 92

3.4.3 The Quantitative Impact of Goods Market Frictions . . . . . . . . . . . . . . . . 93

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

CONTENTS vii

A Appendix to Chapter 1 99

A.1 Solving for the Optimal Contract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

A.2 Additional Results: Bank Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

A.3 Additional Results: Management Monitoring . . . . . . . . . . . . . . . . . . . . . . . . 106

A.4 Tests of Additional Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

B Appendix to Chapter 2 119

B.1 Substitutability and Price Externalities . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

B.1.1 Stage Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

B.1.2 Infinitely-Repeated Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

B.2 Definitions and Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

B.2.1 Definitions and Proofs from Sections 2.2 and 2.3 . . . . . . . . . . . . . . . . . . 124

B.2.2 Proofs from Appendix B.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

B.3 Computational Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

C Appendix to Chapter 3 139

C.1 Cointegration Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

C.2 Advertising Expenditures and Long-Run Risk . . . . . . . . . . . . . . . . . . . . . . . 142

C.3 Derivation of the Stochastic Discount Factor . . . . . . . . . . . . . . . . . . . . . . . . . 144

C.4 Computational Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

List of Tables

1.1 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.2 The Policy Effect on Bank Shareholder Value . . . . . . . . . . . . . . . . . . . . . . . . 19

1.3 Robustness and Placebo Tests: Tobin’s q . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.4 The Policy Effect on Bank Professional Expenditure . . . . . . . . . . . . . . . . . . . . 24

1.5 Professional Expenditure Growth and Post-Treatment Value Losses . . . . . . . . . . . 26

1.6 Managerial Rents: Earnings Smoothing in the Financial Crisis . . . . . . . . . . . . . . 29

1.7 Cash Flow Risk, Shareholder Value, and Professional Expenditures . . . . . . . . . . . 30

1.8 Ownership, Management Monitoring, and Value . . . . . . . . . . . . . . . . . . . . . . 31

3.1 Summary Statistics for Predictors, Post-War Period . . . . . . . . . . . . . . . . . . . . 76

3.2 Consumption Growth and Excess Returns Predictability, Post-War Period . . . . . . . 77

3.3 Excess Returns Predictive Regressions, Post-War Period . . . . . . . . . . . . . . . . . . 78

3.4 Tri-Variate Excess Returns Predictive Regressions, Post-War Period . . . . . . . . . . . 79

3.5 VAR Model for Advertising and Consumption Growth, Post-War Period . . . . . . . . 80

3.6 VAR Model for Advertising and Consumption Growth, 1922-2009 and 1982-2009 . . . 81

3.7 Consumption Growth Predictive Regressions, Post-War Period . . . . . . . . . . . . . 82

ix

x LIST OF TABLES

3.8 Out-of-Sample Excess Returns Predictive Regressions . . . . . . . . . . . . . . . . . . . 85

3.9 Model-Simulated Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.10 Results: Returns Predictability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

3.11 Predictability in the Centralized Economy . . . . . . . . . . . . . . . . . . . . . . . . . . 96

A1 Robustness and Placebo Tests: Market-to-Book . . . . . . . . . . . . . . . . . . . . . . . 101

A2 Bank Size Manipulation Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

A3 Event Study Around Policy Date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

A4 Additional Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

A5 Quarterly Treatment Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

A6 Falsification Tests: Non-Fed-Regulated Firms . . . . . . . . . . . . . . . . . . . . . . . . 105

A7 Triple Differences: Policy Effect on Market-to-Book . . . . . . . . . . . . . . . . . . . . 106

A8 Audit Fees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

A9 Internal Controls and Post-Treatment Professional Expenditure . . . . . . . . . . . . . 108

A10 SEC Accelerated Filers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

A11 Summary Statistics: Funding Costs, Profitability, and Earnings Smoothing . . . . . . . 110

A12 Funding Costs and Earnings Smoothing: Robustness and Placebo . . . . . . . . . . . . 111

A13 Robustness: Cash Flow Risk, Shareholder Value, and Professional Expenditure . . . . 112

A14 Chairman Ownership and Professional Expenditure Persistence . . . . . . . . . . . . . 113

A15 Chairman Ownership and Market-to-Book Discount Persistence . . . . . . . . . . . . . 114

A16 Government Tail Risk Insurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

A17 Voluntary Reporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

A18 Liquidity, Volatility, and Market Frictions . . . . . . . . . . . . . . . . . . . . . . . . . . 117

A19 Leverage and Capital Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

C1 Philips-Ouliaris and Johansen Tests for Cointegration . . . . . . . . . . . . . . . . . . . 141

C2 Vector-Error-Correction Model for Consumption Growth Predictions, Post-War Period 142

List of Figures

1.1 Common Trends in Pre-Policy Bank Valuation . . . . . . . . . . . . . . . . . . . . . . . 17

1.2 Bank Size Manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.1 Equilibrium Value Sets and Group Punishments . . . . . . . . . . . . . . . . . . . . . . 62

2.2 Input Substitutability and the Welfare Impact of Group Punishments . . . . . . . . . . 64

3.1 Expenditures in Physical and Non-Physical Advertising in the U.S., 1950-2010 . . . . . 72

3.2 Per-Capita Consumption and Advertising in the U.S., 1950-2010 . . . . . . . . . . . . . 73

3.3 Advertising Expenditures Growth, Consumption Growth and Excess Returns in theU.S., 1950-2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.4 Coefficient Estimates in Out-of-Sample Excess Returns Predictive Regressions, 1980-2010 84

3.5 Customer Capital Investment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

B1 Comparative Statics: Marginal Cost of Production and Welfare . . . . . . . . . . . . . . 124

xi

Chapter 1

The Value of Regulators as Monitors:Evidence from Banking

1

2 CHAPTER 1. THE VALUE OF REGULATORS AS MONITORS: EVIDENCE FROM BANKING

1.1 Introduction

A common view in the banking industry is that financial regulation has a negative impact on share-

holder value: regulatory compliance subtracts resources from lending and deposit-making activities,

reduces profits, and ultimately hurts investors. As a result, the recent decline of small and medium-

sized banks in the United States has often been attributed to regulation, and regulatory burden re-

duction for small banks is now a priority on the agenda of the US Federal Reserve (the Fed). In a

recent testimony to the House Financial Services Committee, the Chair of the Fed Board of Gover-

nors Janet Yellen stated: “With respect to small and medium-sized banks, we must build on the steps we have

already taken to ensure that they do not face undue regulatory burdens.”1 While the current policy discus-

sion highlights the costs of financial regulation for bank investors, agency theory suggests a positive

role for regulation in reducing the costs incurred by shareholders to monitor bank mangement.

In this paper, I exploit the regulatory environment of US Bank Holding Companies (BHCs) to study

the value impact of regulatory monitoring.2 The US Federal Reserve (the Fed) is the primary re-

gulator of BHCs, and a pervasive component of the Fed’s monitoring activity is the collection and

analysis of BHC financial statements. Both the frequency and the volume of BHC reporting to the

Fed are based on a fixed asset size threshold, such that smaller BHCs falling below the threshold are

exempted from most of the reporting requirements faced by larger BHCs above the threshold. I use

a 2006 Fed policy raising this size threshold as a shock to regulatory monitoring, and study changes

in bank value around the new threshold in a regression discontinuity design. My identification stra-

tegy comes from the quasi-random assignment of treated banks just below the threshold and control

banks just above the threshold before the Fed implements its policy, such that any systematic value

difference after the policy implementation is only due to differences in regulatory monitoring.

Following the predictions of agency theory, I interpret the change in Fed regulatory monitoring as a

shock to shareholder monitoring costs. To provide a structure to my empirical tests, I build a stylized

model of monitoring in the class of Townsend (1979), and derive three key predictions on the impact

1Yellen (2016).2Even if a BHC can include more than one bank, I will use the two terms interchangeably in the rest of the paper.

1.1. INTRODUCTION 3

of monitoring costs on shareholder value. In the model, a manager has private incentives to mis-

report bank cash flows and a shareholder can pay a monitoring cost to verify the cash flows reported

by the manager. When monitoring costs are small, the shareholder always monitors and extracts

the entire surplus from the bank. As monitoring becomes more expensive (as for treated banks),

shareholder value drops due to increased monitoring expenditures and increased managerial rents.

The first model prediction is therefore that reduced regulatory monitoring should lead to shareholder

value losses.

My main finding is consistent with the first prediction of the model: I show that, relative to control

banks, treated banks experience a 1% decrease in Tobin’s q (the market value of bank assets divided

by the book value of bank assets) and a 7% decrease in Market-to-Book (the market-to-book value of

bank equity) after the treatment. The finding is robust across a number of empirical specifications,

sample restrictions, placebo tests, and falsification tests. For example, the treatment effect is stronger

around the policy implementation date and threshold and disappears when I use arbitrary placebo

dates and thresholds to separate treatment and control groups, reducing sample selection concerns.

Moreover, my estimate of the treatment effect is not driven by pre-existing differences in valuation

across treated and control groups, and it is not biased by pre-treatment size manipulation.3 Impor-

tantly, the finding is not driven by changes in government bailout guarantees (Gandhi and Lustig

(2015)), financial disclosure (Hutton, Marcus, and Tehranian (2009)), stock liquidity and volatility,

and other size-based regulations implemented by the Fed at the beginning of 2006.

The second model prediction is that the value losses experienced by treated banks should be due

to increased monitoring expenditures and increased managerial rents. In line with this prediction,

I show that treated banks experience a 25% increase in their professional expenditures after the tre-

atment. These professional expenditures are largely related to bank internal controls, and strongly

correlated with post-treatment losses in shareholder value. Moreover, during the financial crisis

banks below the policy implementation threshold engage in more aggressive earnings smoothing

than banks above the threshold, confirming the prediction of increased managerial rents (Fudenberg

3Reporting exemptions are based on June 2005 BHC assets, but the threshold change is first announced by the Fed onlyin November 2005. Additionally, McCrary (2008) tests show no evidence of pre-treatment asset size manipulation.


and Tirole (1995)). Specifically, banks below the threshold decrease their Loan Loss Provisions (LLPs)

by more than banks above the threshold, and these LLP changes are due to managerial discretion

rather than to bank performance.

The third model prediction is that value losses and monitoring expenditures in treated banks should

both be positively correlated with the risk of their unobservable cash flows. Intuitively, high cash

flow risk increases the likelihood of tail states where cash flows are low or managerial rents are high,

decreasing bank value and increasing the marginal value of monitoring. Empirically, I proxy the risk

of unobservable cash flows with the absolute difference between analyst-forecasted and realized

bank profitability. I find that treated banks with high cash flow risk experience larger value losses

and professional expenditure growth than banks with low expected cash flow risk.

Finally, I argue that the increased monitoring costs faced by treated banks’ shareholders increase their

incentives to free-ride on each other’s monitoring (Grossman and Hart (1980), Holmstrom (1982)).

Consistent with Shleifer and Vishny (1986), the presence of a large shareholder—the board chair-

man—helps to mitigate shareholder free-riding problems after the treatment. I show that treated

banks with high chairman ownership experience higher professional expenditure growth and larger

value losses than treated banks with low chairman ownership. Moreover, post-treatment professi-

onal expenditure growth is more persistent and value drops are less persistent in banks with high

chairman ownership.

Overall, my paper is among the first to quantify the shareholder value of monitoring. Quantitatively,

I attribute around sixty percent of the loss in shareholder value for deregulated banks to increased

monitoring expenditure and managerial rents, and I attribute around forty percent of the loss to

increased free-riding problems. I conclude that regulation can be value-increasing for shareholders

when regulators monitor the management. My results are potentially applicable to other heavily-

regulated industries besides the banking industry, and provide new evidence against the standing

consensus that financial regulation negatively affects bank shareholders.

1.1. INTRODUCTION 5

Related Literature A long-standing question in financial economics is the extent to which moni-

toring affects shareholder value. Motivated by theoretical arguments (Shleifer and Vishny (1986),

Kahn and Winton (1998), Maug (1998)), the literature has traditionally focused on institutional ow-

nership as a measure of monitoring to estimate the impact of monitoring on firm value (McConnell

and Servaes (1990), Ferreira and Matos (2008)). Causal inference is however difficult in these studies,

because firm ownership and value are endogenously determined by firms’ contracting environment

(Himmelberg, Hubbard, and Palia (1999), Coles, Lemmon, and Meschke (2012)). My paper contribu-

tes to this literature by using a novel identification strategy to estimate a large and positive impact of

monitoring on value. To the best of my knowledge, my paper is the first to test the predictions of a

traditional class of monitoring models (Townsend (1979), Gale and Hellwig (1985)), and among the

first to show that monitoring is valuable because it reduces managerial rent-seeking.4

Theoretical and emprical research shows that agency frictions are particularly severe in the context of

banking. The risk profile of bank assets is difficult to observe by outsiders and easy to modify by in-

siders (Morgan (2002), Dang, Gorton, Holmstrom, and Ordonez (2017)), and deposit insurance gives

bank lenders low incentives to monitor the management (Gorton and Pennacchi (1990)). Moreover,

deposit insurance and other bank regulations might distort shareholder incentives to take risk (Mer-

ton (1977)), possibly in contrast with managerial preferences (Saunders, Strock, and Travlos (1990)).

Previous empirical work has argued that agency frictions and managerial rent-seeking can have a

negative impact on bank value (Laeven and Levine (2007), Goetz, Laeven, and Levine (2013)). My

work provides causal evidence on the impact of agency frictions on bank value, and demonstrates

regulatory monitoring as an effective tool to mitigate these frictions.

The recent crisis has stimulated academic interest in the costs and benefits of financial regulation.

While many papers show that financial regulation is positively related to bank efficiency (Barth, Lin,

Ma, Seade, and Song (2013)), and negatively related to bank risk-taking and failure (Agarwal, Lucca,

Seru, and Trebbi (2014), Hirtle, Kovner, and Plosser (2016), Kandrac and Schlusche (2017)), a recent

4In this respect, my results are close to Bertrand and Mullainathan (2003), Kempf, Manconi, and Spalt (2016), andSchmidt and Fahlenbrach (2017), who focus on different outcome variables to show that monitoring reduces rent-seeking.Falato, Kadyrzhanova, and Lel (2014) show a positive impact of monitoring on firm value, but are silent about the specificmechanism through which monitoring increases value.


study by Buchak, Matvos, Piskorski, and Seru (2017) shows that bank regulatory burden is one of

the main reasons for the raise of shadow banking. My paper adds to this literature by providing the

first estimate of the value of monitoring by financial regulators.

1.2 Institutional Background and Motivating Theory

The banking industry provides an ideal laboratory to study the impact of regulatory monitoring on

shareholder value. A common view in the banking industry is that regulatory burden is particularly

detrimental to bank profitability and value, and financial regulation is a commonly-cited reason

for the decline of small banks in the United States. This view gained momentum among financial

authorities since the Dodd-Frank Act of 2010, and small bank regulatory burden reduction is now

an important priority on the policymaker’s agenda (Yellen (2016)). While the costs and benefits of

financial regulation are yet not fully understood, agency theory predicts that financial regulation can

have a positive impact on bank value by reducing shareholder monitoring costs.

1.2.1 Institutional Background

The Bank Holding Company Act of 1956 broadly defines a BHC as any company that owns and/or

has control over one or more banks. Commercial banks in the United States are not mandated to

be part of a BHC structure. However, being part part of a BHC offers substantial benefits, such as

increased flexibility in raising external financing and acquiring other banks, as well as the ability to

acquire non-bank subsidiaries. In practice, these benefits are such that at the end of 2016 around

eighty-four percent of commercial banks in the US were part of a BHC.5

The benefits of being part of a BHC come at the cost of compliance with the regulatory and supervis-

ory requirements imposed by the Fed. From a regulatory standpoint, Regulation Y from 1980 gives

the Fed exclusive jurisdiction in establishing BHC capital requirements, regulating BHC mergers

5https://www.fedpartnership.gov/bank-life-cycle/grow-shareholder-value/bank-holding-companies.

https://www.fedpartnership.gov/bank-life-cycle/grow-shareholder-value/bank-holding-companies

1.2. INSTITUTIONAL BACKGROUND AND MOTIVATING THEORY 7

and acquisitions, and defining and regulating non-banking activities performed by BHC subsidia-

ries. From a supervisory standpoint, Section 5 of the Bank Holding Company Act provides guidance

for the off-site and on-site inspections regularly conducted by regional Fed officials under delegated

authority from the Board.

The main information source for Fed off-site inspections is a set of financial statements collected

and reviewed by the Fed on a regular basis. In practice, specialized teams of Fed officials focus on

the analysis and cross-bank comparison of these statements to monitor the safety and soundness of

individual banks, and to identify potential threats to the financial system (Eisenbach, Haughwout,

Hirtle, Kovner, Lucca, and Plosser (2017)). The process through which the Fed collects financial sta-

tements is different for large and small BHCs. Large BHCs need to file every quarter consolidated

financial statements (form FR Y-9C) and holding parent company statements (FR Y-9LP) which con-

tain detailed balance sheet, income statement, and off-balance sheet information about the bank’s

activity. To avoid reporting burden, the Fed allows smaller BHCs to only file an annual statement

for the holding parent company (FR Y-9SP), such that small BHCs face substantially lower reporting

requirements than large BHCs.

The Fed separates small and large reporting BHCs based on a fixed, bank-independent asset size

threshold. From 1986 until the end of 2005, this size threshold was set to $150 million in total assets.

In March 2006, the Fed implemented a regulation increasing the threshold to $500 million (regulation

71-FR-11194), therefore providing new reporting exemptions to all BHCs with assets between $150

and $500 million. I use this change in reporting requirements as a shock to the monitoring costs of

deregulated banks’ shareholders.

1.2.2 Predictions from Agency Theory

What kind of responses can be expected following a shock to shareholder monitoring costs? In this

section I use the lens of a classic model of monitoring (Townsend (1979)) to derive three key testable

predictions and provide structure to the empirical tests of the rest of the paper.


There are two agents in the model, a penniless manager and a shareholder with deep pockets. The

manager and the shareholder are both risk-neutral, and the risk-free rate is zero. The manager has

monopoly access to a project with cost I, which will generate a random cash flow y ∈[

¯y, y]⊆ R+

with cdf F and pdf f at the end of the period. The project has positive NPV, which I denote by Vf :

Vf =∫ y

¯y

ydF (y)− I > 0. (1.1)

The manager costlessly observes the realized project cash flow, and must report the cash flow to

shareholder. The manager can consume the difference between the realized cash flow and the cash

flow that she reports to the shareholder, and therefore has an incentive to under-report to the share-

holder. On the other hand, the shareholder can pay an audit cost k to perfectly observe the realized

cash flow.

The shareholder has full bargaining power, and her problem is to maximize her expected profits

while eliciting truthful cash flow revelation by the manager. Resorting to the revelation principle, I

characterize contracts in which the manager always reveals the true cash flow. A contract is then a

couple {π (y) , m (y)} that specifies payments from the manager to the shareholder π (y) :[

¯y, y]→

R and monitoring decisions m (y) :[

¯y, y]→ {0, 1} as functions of the cash flow reported by the

manager. I assume that audits are deterministic, in the sense that for all y, m (y) is either 0 or 1. This

partitions the set[

¯y, y]

in a region where the shareholders always audits the manager and a region

where the shareholder never audits the manager.

The shareholder maximizes her expected profits

∫ y

¯y[π (y)−m (y) k] dF (y)− I, (1.2)

subject to the manager’s participation constraint

∫ y

¯y[y− π (y)] dF (y) ≥ 0, (1.3)

the manager’s limited liability constraint that, for all y,

y ≥ π (y) , (1.4)

1.2. INSTITUTIONAL BACKGROUND AND MOTIVATING THEORY 9

and the incentive-compatibility constraints ensuring that the manager always reveals the true cash

flow. For the contract to be incentive-compatible, the following conditions must be verified. First, in

the non-monitoring region the shareholder must always receive a constant payment P.6 This allows

to write the payment π (y) as

π (y) = (1−m (y)) P + m (y)π1 (y) , (1.5)

where π1 (y) is the payment in the monitoring region. Second, to prevent the manager to report cash

flows in the non-monitoring region when the observed cash flow is in the monitoring region, it must

be that

m (y)π1 (y) ≤ P. (1.6)

Constraints (1.5) and (1.6) characterize incentive-compatibility by the manager. The shareholder’s

problem then becomes finding m (y) and π1 (y) to maximize her expected profits, subject to con-

straints (1.3)-(1.6).

In the appendix, I solve for the optimal contract. As in Gale and Hellwig (1985), the optimal contract

is such that the monitoring region is the low cash flow region for which π (y) = y < P, and the non-

monitoring region is the high cash flow region for which y ≥ π (y) = P. In the monitoring region, the

shareholder pays the monitoring cost k and the manager gives all the cash flow to the shareholder.

In the non-monitoring region, the shareholder receives the fixed payment P and the manager keeps

y− P.

Finally, conditional on the optimal contract, the optimal fixed payment P∗ is chosen by the sharehol-

der to solve the unconstrained maximization problem

maxP

∫ P

¯y

(y− k) dF (y) + P (1− F (P))− I. (1.7)

6If for some cash flow realization in the monitoring region the contract specifies a lower payment to the shareholderthan for other realizations in the monitoring region, there is an incentive for the manager to report the cash flow associatedwith the lower payment.


Taking the first-order conditions of this problem and re-arranging, I get

1− F (P∗) = k f (P∗) , (1.8)

showing that at the optimum, the shareholder balances the benefits of increasing P coming from

reduced managerial rents with the costs coming from increased monitoring.

The first testable prediction of the model therefore comes from inspection of Equation (1.8), by noting

that as the monitoring cost k becomes small, the probability F (P∗) that the shareholder monitors the

manager approaches one. In other words, when monitoring is inexpensive the shareholder always

monitors and extracts the entire NPV from the project.

Prediction 1. An increase in shareholder monitoring costs leads to shareholder value losses.

Next, let Vc denote shareholder value when monitoring is costly (i.e. k > 0):

Vc =∫ P∗

¯y

(y− k) dF (y) + P∗ (1− F (P∗))− I. (1.9)

The loss in shareholder value from a world where monitoring is costless and the shareholder extracts

the entire project NPV is then

Vf −Vc = kF (P∗) +∫ y

P∗(y− P∗) dF (y) , (1.10)

which consists of monitoring expenditures and managerial rents.

Prediction 2. When shareholder monitoring costs increase, losses in shareholder value are due to increased

monitoring expenditure and managerial rents.

The last model prediction requires assumptions on the distribution of bank cash flows. To provide

intuition, I assume that cash flows are uniformly distributed over the interval[

¯y, y]. The model

generates similar predictions for other types of distributions (e.g. lognormal). Using a uniform

distribution, some simple algebra shows that the shareholder value loss (1.10) becomes

Vf −Vc = k

(1− 1

2k

y−¯y

), (1.11)

1.3. EMPIRICAL SETTING 11

which is increasing in the term y −¯y. Noting that expected monitoring expenditure, kF (P∗), is

also increasing in y−¯y, and that y−

¯y is proportional to cash flow risk, the last prediction directly

follows.7

Prediction 3. When shareholder monitoring costs increase, shareholder value losses and monitoring expendi-

ture are increasing in cash flow risk.

Intuitively, when cash flow risk increases the likelihood of states where income is low or managerial

rents are high increases, and this reduces shareholder value relative to a world where monitoring is

costless and the manager cannot extract any rents. Over the next few sections I show that regulatory

monitoring reduces shareholder monitoring costs by testing the predictions of my stylized model in

the data.

1.3 Empirical Setting

In this section I describe how I measure bank value, monitoring expenditure, and cash flow risk

in the data, and describe how I use these variables to estimate the shareholder value of regulatory

monitoring.

1.3.1 Data Sources and Measurement

The data on BHC total consolidated assets comes from the Federal Reserve Regulatory Dataset. This

dataset is publicly available on the Federal Reserve of Chicago’s website, and contains information

directly coming from the FR Y-9C, FR Y-9LP, and FR Y-9SP reports. I use the dataset to categorize

BHCs into treated and control groups based on their 2005 average consolidated assets, and to keep

track of which BHCs file which forms in each quarter.8 Since the Fed policy allows treated banks to

stop reporting their FR Y-9C consolidated statements, I use Compustat Bank as my main source of

7The standard deviation of a uniform distribution with support [a, b] is given by (b− a) /√

12.8This is important because, as I show in Section 1.6, some BHCs voluntarily keep filing forms FR Y-9C and FR Y-9LP

even if their total assets are below $500 million after the treatment.


BHC consolidated financial data. I combine this dataset with CRSP to obtain end-of-quarter BHC

market-to-book values, and in turn merge the Compustat-CRSP combined dataset with the Federal

Reserve Regulatory Dataset using the link table available on the Federal Reserve of New York’s

website. Finally, I obtain data on analyst forecasts of bank profitability from I/B/E/S.

The observation frequency is quarterly, starting with the first quarter of 2004 and ending with the

last quarter of 2007. Within this time period, I construct my main sample as follows. I focus on top-

tier BHCs (defined as in Goetz, Laeven, and Levine (2016)) with average 2005 total assets between

$150 and $850 million, and with stock price data available on CRSP. I assign individual BHCs to the

treated group if their average total assets in 2005 are between $150 million and $500 million, and to

the control group if their average total assets in 2005 are between $500 million and $850 million.9

The final sample consists of 2,780 observations on 208 distinct BHCs, out of which 108 belong to the

treated group and 100 belong to the control group. These BHCs represent around ten percent of the

total number of BHCs in the US at the end of 2005, and around forty-six percent of the BHCs listed

on the stock market at the end of 2005. In terms of size, these banks represent around one percent of

the total assets in the banking sector at the end of 2005, and around five percent of the assets in the

bottom ninety-nine percent of the asset distribution. Finally, the average pre-treatment BHC asset

size in my sample is $519 million, right above the policy implementation threshold.

Table 1.1 reports summary statistics for my main measures of bank value, monitoring expenditure,

and cash flow risk, both in the full sample and in the treated and control sub-samples.10 The first

two rows of Panel A show summary statistics for my measures of bank shareholder value, Tobin’s

q and the Market-to-Book ratio of bank equity. The data shows little dispersion in these valuation

ratios, both within the main sample and across the treated and control sub-samples. The average

and median Tobin’s q in the main sample are 1.07 and 1.06, respectively, and the average and median

Market-to-Book are 1.75 and 1.65.

9I choose the upper bound of $850 million in total assets in such a way that the final treated and control samples containapproximately the same number of banks. In Section 3.2.2, I use $1 billion and $1.5 billion as alternative upper bounds,and show that the main results of the paper are not sensitive to these choices.

10Since I only observe evidence of managerial rents during the financial crisis, I leave a description of how I measurethese rents to Section 1.5.1.


Table 1.1

Summary Statistics

This table reports summary statistics for the variables in the paper, both in the main sample and in the treatedand control sub-samples. In Panel A, Tobin’s q is the market value of total assets (market value of equityplus book value of debt) divided by the book value of total assets. Market-to-Book is the market value ofequity divided by the book value of equity. Professional Services are fees paid to management consultingfirms, investment banks, and auditing firms, in millions of US dollars. Cash flow risk is a quarterly averageof the absolute difference between monthly analyst consensus forecast of two-year-forward bank EPS and therealized EPS value corresponding to each consensus forecasts. In Panel B, leverage is total liabilities divided bytotal assets, Tier 1 Ratio is Tier 1 Capital divided by Risk-Weighted Assets, Profitability is net income dividedby net interest income, and ROE is net income divided by book value of equity. Total Assets are reported inmillions of US dollars. Finally, diversification is non-interest income divided by net interest income, and assetgrowth is quarterly growth in BHC total assets.

Panel A: Shareholder Value, Monitoring Expenditure, and Cash Flow Risk

Full Sample Treated Control

N Mean Med. SD N Mean Med. SD N Mean Med. SD

Tobin’s q 2,623 1.07 1.06 0.05 1,329 1.06 1.06 0.05 1,294 1.07 1.06 0.05Market-to-Book 2,623 1.75 1.65 0.57 1,329 1.71 1.60 0.57 1,294 1.80 1.72 0.56Professional Fees 1,756 0.14 0.10 0.16 862 0.13 0.10 0.14 894 0.16 0.12 0.18Cash Flow Risk 937 0.87 0.24 2.38 306 1.54 0.34 3.80 631 0.55 0.22 1.04

Panel B: Additional Variables

Full Sample Treated Control


Leverage 2,624 0.91 0.91 0.03 1,329 0.91 0.91 0.03 1,295 0.91 0.91 0.02Tier 1 Ratio 2,289 0.12 0.12 0.03 1,096 0.13 0.12 0.04 1,193 0.12 0.11 0.03Total Assets 2,703 554.9 535.6 232.5 1,341 386.5 382.8 128.5 1,362 720.6 696.8 188.8Profitability 2,701 0.23 0.26 0.34 1,340 0.20 0.24 0.44 1,361 0.25 0.27 0.19ROE 2,624 0.02 0.03 0.03 1,329 0.02 0.02 0.03 1,295 0.03 0.03 0.02Diversification 2,701 0.27 0.22 0.24 1,340 0.26 0.20 0.29 1,361 0.27 0.24 0.18Asset Growth 2,655 0.03 0.02 0.06 1,308 0.03 0.02 0.06 1,347 0.03 0.02 0.05


The third row of Panel A shows summary statistics for bank professional expenditures, in millions

of US dollars. These expenditures are recorded as a separate item on bank income statements, and

include fees paid to consultants, auditors, and investment bankers. In Section 1.5.1, I show that

professional expenditures are a good proxy for shareholder monitoring in my sample, because they

are mostly related to the implementation of internal controls. Banks in the treated group pay slightly

lower professional fees than banks in the control group. On average, treated banks spend 0.13 million

of dollars per quarter in professional services, with a standard deviation of 0.14 million. Control

banks spend on average 0.16 million of dollars per quarter in professional services, with a standard

deviation of 0.18 million.

The last row of Panel A finally presents my primary cash flow risk measure, the absolute difference

between analyst consensus forecast of two-year-forward bank EPS and the realized EPS value corre-

sponding to each consensus forecast. By construction, this variable provides a time-varying measure

of analyst uncertainty about future bank profitability, and therefore represents a close approximation

to the risk of unobservable cash flows in my model. The table shows that cash flow risk is on average

higher for treated banks than for control banks, partially reflecting lower analyst coverage of small

banks. Both before and after the treatment, the average treated bank is covered by approximately

four analysts analysts in a given quarter, while the average control bank is covered by six analysts.

Panel B of Table 1.1 reports summary statistics for the other key variables in the paper, which I

borrow from the literature as potential determinants of cross-sectional heterogeneity in bank value

(Laeven and Levine (2007), Minton, Stulz, and Taboada (2017)). These variables include leverage

(total liabilities minus noncontrolling interest divided by total assets), the regulatory Tier 1 Regula-

tory Capital Ratio (henceforth Tier 1 Ratio, the bank self-reported ratio of Tier 1 Capital divided by

Risk-Weighted Assets), total assets, profitability (net income divided by net interest income), Return

on Equity (ROE, net income divided by book value of equity), diversification (noninterest income

divided by net interest income), and quarterly asset growth. As in Panel A, the data reveals little

differences in these variables across treated and control groups, thus confirming the comparability

of these two sets of banks.


1.3.2 Estimation Strategy and Identification

In this section, I describe my strategy to test the model predictions in the data and to measure the

shareholder value of regulatory monitoring. I exploit the change in regulatory reporting require-

ment to the Fed as a quasi-natural source of variation in shareholder monitoring costs. My empiri-

cal strategy consists in comparing the value and monitoring expenditure of smaller, treated banks

with pre-treatment total assets just below $500 million with the value of larger, control banks with

pre-treatment total assets just above $500 million, before and after the treatment. More precisely, I

estimate the model

Yit = β0 + β1 (Postt × Treatedi) + β2Xit + γi + δt + εit, (1.12)

where Yit is an outcome variable (e.g. Tobin’s q) for BHC i in quarter t, Postt is an indicator equal

to one if quarter t follows the last quarter of 2005 and zero otherwise, Treatedi is an indicator equal

to one if the average assets of BHC i during 2005 are just below $500 million, Xit is a matrix of time-

varying control variables (such as assets and profitability), γi is a time-invariant and BHC-specific

fixed effect, δt is a BHC-invariant and time-specific fixed effect, and εit is a normally-distributed error

term. The coefficient of interest is β1, my estimate of the value difference between treated and control

banks before and after the treatment.

My empirical strategy relies on the key identification assumption of quasi-random assignment of

treated and control banks around the threshold before the Fed changes the reporting requirements of

treated banks, such that any systematic value difference after the policy implementation is arguably

only due to differences in regulatory monitoring. In practice, this assumption can be violated for

two reasons. First, the assumption is violated if the threshold change results from lobbying, making

the treatment an endogenous outcome. Second, the assumption is violated if, even in absence of

lobbying, banks engage in size manipulation around the new threshold before its implementation.

Although the institutional details of the policy suggest that lobbying was unlikely, whether the po-

licy was unanticipated by bank shareholders is ultimately an empirical question.11 In Figure 1.1 I11The first proposal for public comment on the policy dates to November 2005, and the policy was quickly implemented

at the beginning of March 2006 without modifications to the initial proposal.


report a diagnostic test aimed at detecting pre-existing differences in the average valuation of tre-

ated and control banks before the treatment. Panels A and B report these diagnostics for Tobin’s

q and Market-to-Book, respectively, and are constructed as follows. I first divide the sample into

two sub-samples, the pre-treatment sample before the first quarter of 2006 and the post-treatment

sample starting with the first quarter of 2006. In each of these sub-samples, I run a kernel-weighted

local polynomial regression to obtain a smoothed estimate of the trend component of treated and

control banks’ valuation. In Figure 1.1 I then plot these estimated trend components and their as-

sociated confidence intervals as functions of the observation quarter, both in the pre- and in the

post-treatment periods.12 Figure 1.1 shows that the trend components of treated and control banks’

valuation are statistically indistinguishable from each other in the pre-treatment period, supporting

the claim that the threshold change was unanticipated. Moreover, the figure shows an increase in

the difference between treated and control banks’ average valuation after the treatment, providing a

visual preview of the results in the next section.

In Figure 1.2, I report the results of a McCrary (2008) discontinuity test to reduce concerns of bank

size manipulation around the $500 million threshold. Specifically, I construct a finely-gridded his-

togram of bank total assets, which I then smooth on each size of the threshold using local linear

regression. In Figure 1.2, I then report point estimates and 95% confidence intervals of smoothed as-

set densities during the 2005-2007 period (Panel A) and during the four quarters immediately before

the treatment (Panel B). Both before and after the treatment, the estimated asset density below the

threshold is not statistically different from the estimated asset density above the threshold.13 Impor-

tantly, a specific institutional feature of the policy reduces residual concerns of asset manipulation

before the treatment. The policy states that individual BHCs qualify for reporting exemptions only

if their June 2005 consolidated assets are below $500 million. At the same time, the Fed first publicly

announces the threshold change in November 2005, preventing pre-treatment size manipulation.

12I divide the sample to avoid post-treatment observations entering the estimation of the pre-treatment trend, andvice-versa. All panels of Figure 1.1 are constructed using an Epanechnikov kernel and the rule-of-thumb bandwidth sizesuggested in Fan and Gijbels (1996). Different kernel and bandwidth choices generate similar results.

13All the results are calculated using the histogram bin size and local linear regression bandwidth suggested in McCrary(2008).


Figure 1.1

Common Trends in Pre-Policy Bank Valuation

This figure reports a parallel trends diagnostic test on treated and control banks’ Tobin’s q (Panel A) andMarket-to-Book (Panel B). I first divide the sample into two sub-samples, the pre-treatment sample before thefirst quarter of 2006 and the post-treatment sample starting with the first quarter of 2006. In each of thesesub-samples, I run a kernel-weighted local polynomial regression to obtain a smoothed estimate of the trendcomponent of valuation. The local polynomial regression uses an Epanechnikov kernel and the rule-of-thumbbandwidth suggested in Fan and Gijbels (1996). The figure reports point estimates and 95% confidence in-tervals of the trend component of treated and control banks’ valuation as functions of the estimation quarter.Tobin’s q and Market-to Book are defined as in Table 1.1.

1.02

1.04

1.06

1.08

1.1

Policy Change

2004q1 2005q1 2006q1 2007q1 2008q1

Control 95% C.I.Treated 95% C.I.

Panel A: Tobin's q

1.2

1.4

1.6

1.8

2

Policy Change

2004q1 2005q1 2006q1 2007q1 2008q1

Control 95% C.I.Treated 95% C.I.

Panel B: Market-to-Book Ratio


Figure 1.2

Bank Size Manipulation

This figure shows point estimates and 95% confidence intervals of the smoothed cross-sectional density ofbank total assets during the 2005-2007 period (Panel A) and during the four quarters preceding the Policy(Panel B). The goal of the figure is to detect discontinuities indicative of size manipulation around the Policythreshold. The smoothed densities are obtained by first constructing finely-gridded histograms of the cross-section of bank total assets, and by then smoothing the histograms on each size of the threshold using locallinear regression. The optimal histogram bin size and local linear regression bandwidth are calculated usingthe procedure in McCrary (2008).

0.0

005

.001

.001

5.0

02.0

025

Policy Threshold

0 500 1000 1500 2000Total Assets (USD Millions)

Panel A: 2005-2007 BHC Asset Density

0.0

005

.001

.001

5.0

02.0

025

Policy Threshold

0 500 1000 1500Total Assets (USD Millions)

Panel B: 2005 BHC Asset Density

1.4 The Value of Regulatory Monitoring

In this section I present my main results on the value impact of regulatory monitoring.

1.4.1 Main Results

Table 1.2 shows my main findings on the value impact of regulatory monitoring. The table reports

point estimates for the coefficients in Equation (1.12), along with their standard errors (clustered at

the BHC-level). The main coefficient of interest is associated with the “Post × Treated” term, which

represents an estimate of the percentage change in Tobin’s q and Market-to-Book due to the change

in reporting requirements.

When I estimate Equation (1.12) only including quarter- and BHC-level fixed effects, the policy treat-

ment leads to a one percent decline in treated bank Tobin’s q, relative to control banks. The economic

1.4. THE VALUE OF REGULATORY MONITORING 19

Table 1.2

The Policy Effect on Bank Shareholder Value

This table reports estimates of the treatment effect on bank valuation using the empirical specification in Equa-tion (1.12). The coefficient associated with the “Post × Treated” interaction term captures the percentagechange in treated bank valuation due to the treatment. The table includes year-quarter Fixed Effects (FE)and BHC FE. All the variables are defined as in Table 1.1.

log Tobin’s q log Market-to-Book

(1) (2) (3) (4) (5) (6)

Post × Treated -0.010*** -0.011*** -0.010*** -0.069*** -0.079*** -0.074***(0.00) (0.00) (0.00) (0.03) (0.02) (0.02)

Leverage 0.318*** 0.253** 5.473*** 5.170***(0.12) (0.10) (0.81) (0.68)

Tier 1 Ratio 0.376*** 0.280*** 2.539*** 1.746***(0.08) (0.07) (0.51) (0.48)

log Assets -0.032*** -0.234***(0.01) (0.05)

Profitability -0.004 0.041(0.00) (0.04)

ROE 0.091** 0.292(0.04) (0.47)

Diversification -0.004 -0.054(0.00) (0.04)

Asset Growth -0.006 -0.021(0.01) (0.07)

Year-Quarter FE Yes Yes Yes Yes Yes YesBHC FE Yes Yes Yes Yes Yes YesR-Squared 0.360 0.393 0.418 0.413 0.470 0.503Observations 2,177 2,177 2,177 2,177 2,177 2,177

Note: Standard errors (in parentheses) are clustered at the BHC-level. ***, **, and * respectively denote sta-tistical significance at the 1%, 5%, and 10% levels.


magnitude and statistical significance of the treatment effect are not affected by the inclusion of le-

verage and Tier 1 Ratio, reducing concerns that the effect might be due to contemporaneous changes

in small bank capital requirements (see Section 1.6). Everything else equal, a ten percent increase in

leverage and Tier 1 Ratio are respectively associated to a 3.2 and 3.8 percent increase in Tobin’s q, but

the treatment still induces a 1.1 percent decrease in Tobin’s q after the inclusion of these variables.

Finally, the results are robust to the inclusion of size, profitability, diversification, and asset growth

as additional controls.

In the last three specifications of the table, I repeat the same exercise using Market-to-Book as de-

pendent variable. The table shows that the treatment induces a 6.9 percent loss in Market-to-Book

for treated banks, and this value loss is as high as 7.9 percent when I add time-varying controls to

the specification. To put these numbers in perspective, a seven percent relative decrease in Market-

to-Book corresponds to a $4 million relative decrease in market capitalization for the average treated

bank, implying an aggregate market capitalization loss of approximately $430 million. Finally, a

comparison of the first three and the last three columns of Table 1.2 shows that the treatment effect

on Tobin’s q is almost one order of magnitude smaller than the treatment effect on Market-to-Book.

This is due to leverage, which reduces the impact of equity fluctuations on the market value of bank

assets.14 Overall, the results of the table are consistent with the prediction that increased monitoring

costs reduce bank shareholder value.

14A simple example can illustrate this point. Respectively define by Et, Dt and Mt the book value of equity, the bookvalue of debt and the market value of equity in quarter t. Suppose that Et and Dt do not change between quarter t andquarter t + 1 (i.e. Et = Et+1 ≡ E and Dt = Dt+1 ≡ D), but Mt changes to Mt+1. Let ∆Mt+1 ≡ Mt+1 −Mt. Finally, let mbt andqt respectively define the Market-to-Book ratio and Tobin’s q at time t. The change in Market-to-Book between time t andt + 1 is given by

∆mbt+1 =Mt+1Et+1

− MtEt

=∆Mt+1

E. (1.13)

Then, changes in Tobin’s q can be expressed as a function of changes in Market-to-Book and bank leverage:

∆qt+1 =Mt+1 + Dt+1Et+1 + Dt+1

− Mt + DtEt + Dt

=∆Mt+1E + D

=(

1− DE + D

)∆mbt+1, (1.14)

where the term in parentheses in (1.14) is on average equal to 9% in my sample.

1.4. THE VALUE OF REGULATORY MONITORING 21

1.4.2 Robustness, Placebo, and Falsification Tests

Table 1.3 reports two sets of tests aimed at reducing sample selection concerns. In the interest of

space, I only present results for Tobin’s q, leaving the results for Market-to-Book to the appendix.

In Panel A, I test the impact of different sample bandwidth restrictions on my main result. In the

first four specifications of the table, I use two small samples of BHCs with average 2005 total assets

between $400 and $600 million, and between $300 and $700 million. In the last four specifications,

I conversely use two large samples of BHCs with total assets between $150 million and $1 billion,

and between $150 million and $1.5 billion. To mitigate the impact of confounding factors at the onset

of the financial crisis as the sample size changes, the results in Table 1.3 only include data for 2005

and 2006. The table shows that the main results of the paper are not sensitive to different sample

bandwidth choices. Moreover, the first four specifications—which measure the treatment effect on

banks closest to the threshold—show that the treatment leads to an average 1.2 percent discount in

Tobin’s q, slightly larger than the effect found in Table 1.2.

In Panel B I conversely show that the statistical and economic magnitude of my results disappear

when I separate treated and control banks using arbitrary treatment thresholds and quarters. The

first six specifications show that the results disappear when I use asset thresholds of $300 million,

$750 million and $1 billion to separate treated and control banks. Similarly, Specifications (7) and (8)

show that the results disappear when I use the last quarter of 2004 as treatment quarter, and the last

two specifications show that the results disappear when I use the last quarter of 2006 as treatment

quarter.

In the appendix, I provide additional robustness tests. First, I run an event study to show that the

observed drop in Tobin’s q and Market-to-Book are driven by a drop in the market value of treated

banks as opposed to an increase in their book value or an increase in the market value of control

banks. Second, I apply different restrictions on my sample to include the financial crisis, exclude

banks that drop out of the sample, and exclude banks that are not listed on the stock market before

the policy. Again, my results are robust to these restrictions. Third, I show that the treatment effect

on bank value is roughly uniform at the peak of the business cycle in 2006 and at the beginning of


Table 1.3

Robustness and Placebo Tests: Tobin’s q

This table reports sample bandwidth selection tests (Panel A) and placebo tests (Panel B) on my main Tobin’s qresult. In the first four specifications of Panel A, I use two small samples of BHCs with average 2005 total assetsbetween $400 and $600 million (Specifications (1) and (2)), and between $300 and $700 million (Specifications(3) and (4)). In the last four specifications, I use two large samples of BHCs with total assets between $150 mil-lion and $1 billion (Specifications (5) and (6)), and between $150 million and $1.5 billion (Specifications (7) and(8)). In the first six specifications of Panel B, I use asset thresholds of $300 million, $750 million and $1 billionto separate treated and control BHCs. In Specifications (7) and (8) I use the last quarter of 2004 as treatmentquarter, dropping post-2005 observations from the sample. In the last two specifications, I use the last quarterof 2006 as treatment quarter. The dependent variable in all specifications is the natural logarithm of Tobin’s q.Unreported control variables include leverage, Tier 1 Ratio, total assets, profitability, ROE, diversification, andasset growth.

Panel A: Sample Bandwidth Selection

$400M-600M $300M-700M $150M-1B $150M-1.5B

(1) (2) (3) (4) (5) (6) (7) (8)

Post × Treated -0.012** -0.012** -0.011** -0.012*** -0.010*** -0.012*** -0.011*** -0.012***(0.01) (0.01) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

Controls No Yes No Yes No Yes No Yes

Year-Quarter FE Yes Yes Yes Yes Yes Yes Yes YesBHC FE Yes Yes Yes Yes Yes Yes Yes YesR-Squared 0.117 0.169 0.087 0.131 0.058 0.105 0.046 0.089Observations 355 355 724 724 1,313 1,313 1,611 1,611

Panel B: Placebo Tests

$300M Threshold $750M Threshold $1B Threshold After 12/2004 After 12/2006

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Post × Treated -0.00 -0.00 0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00(0.01) (0.01) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

Controls No Yes No Yes No Yes No Yes No Yes

Year-Quarter FE Yes Yes Yes Yes Yes Yes Yes Yes Yes YesBHC FE Yes Yes Yes Yes Yes Yes Yes Yes Yes YesR-Squared 0.385 0.459 0.339 0.403 0.360 0.422 0.054 0.146 0.351 0.408Observations 1,056 1,056 1,509 1,509 2,076 2,076 1,028 1,028 2,177 2,177


1.5. HOW DOES REGULATORY MONITORING BENEFIT SHAREHOLDERS? 23

the financial crisis in 2007, supporting the validity of my results outside the specific environment of

early 2006. Fourth, using Compustat data I construct two falsification samples of non-financial firms

and non-BHC financial firms (e.g. insurance companies and banks that are not BHCs), and study

whether the valuation of firms with 2005 average total assets just below $500 million changes after

the treatment date, relative to the valuation of firms with total assets just above $500 million. The

results show no evidence of value changes in these falsification samples, confirming that the Fed

threshold change, as opposed to other size-based regulations, drives the drop in treated bank value.

1.5 How does Regulatory Monitoring Benefit Shareholders?

In this section I provide additional evidence for my proposed mechanism by testing the remainng

model predictions, namely that reduced regulatory monitoring increases shareholder monitoring

expenditure and managerial rents, and that bank value losses and monitoring expenditure are po-

sitvely correlated with cash flow risk. Moreover, I show that increased shareholder monitoring costs

increase shareholder incentives to free-ride on each other’s monitoring.

1.5.1 Bank Value, Monitoring Expenditure, and Managerial Rents

The second prediction of the costly state verification model is that the observed losses in treated

bank value should be due to increased shareholder monitoring expenditure and managerial rents.

Table 1.4, provides a first test of this prediction by showing that the policy results in a twenty-five

percent increase in treated bank professional expenditure. This relative professional expenditure in-

crease is economically large for treated banks, amounting to approximately twenty-seven thousand

dollars per quarter or 3.8 percent of the average treated bank’s pre-treatment quarterly net income.

Consistent with the model’s predictions, when I discount these increased professional expenditures

(after-taxes) at an average quarterly ROE of two percent, their discounted present value amounts

to slightly less than a million dollars, around twenty-five percent of the four million relative drop

in market value experienced by the average treated bank. In other words, increased monitoring

expenditures only account for a fraction of the loss in treated bank market value.


Table 1.4

The Policy Effect on Bank Professional Expenditure

This table shows the treatment effect on treated banks’ professional expenditure. In the first three specificationsI use the natural logarithm of professional fees as dependent variable, while in the last three specifications Iuse the natural logarithm of professional fees normalized by net interest income. Additional control variablesnot reported in the table include total assets, profitability, ROE, diversification, and asset growth.

log Professional Fees log Professional FeesNet Interest Income

(1) (2) (3) (4) (5) (6)

Post × Treated 0.259*** 0.267*** 0.244*** 0.225** 0.224** 0.232***(0.09) (0.09) (0.07) (0.09) (0.09) (0.08)

Leverage -2.080 -1.640 2.051 0.885(3.22) (2.49) (3.08) (2.53)

Tier 1 Ratio -4.471*** -2.173 -1.436 -1.290(1.51) (1.34) (1.46) (1.35)

Other Controls No No Yes No No Yes

Year-Quarter FE Yes Yes Yes Yes Yes YesBHC FE Yes Yes Yes Yes Yes YesR-Squared 0.076 0.101 0.182 0.047 0.062 0.129Observations 999 999 999 999 999 999



Next, in Table 1.5, I show that the post-treatment losses in market value are strongly correlated

with professional expenditures. In practice, I augment the main specification of Table 1.2 with an

interaction term for professional expenditures incurred by treated banks only after the treatment,

capturing the post-treatment correlation between treated bank professional expenditure and value.

In most specifications, I include time-varying risk controls such as Z-Score, equity return volatility,

and a tail risk measure borrowed from Ellul and Yerramilli (2013). The table shows that the statistical

significance of the treatment effect is entirely captured by post-treatment professional expenditures

by treated banks. While the magnitude of this triple-differences estimate has no clear economic inter-

pretation, its significance suggests a strong positive correlation between post-treatment professional

expenditure and losses in shareholder value. Moreover, in the appendix I show that this correlation

does not seem to be mechanically driven by changes in profitability, size, or risk variables that are

potentially correlated with both professional expenditure and value.

Finally, a more in-depth analysis reveals that post-treatment professional expenditure growth for tre-

ated banks is mainly related to increased management monitoring, as opposed to other professional

services such as auditing and investment banking. In the appendix, I show that fees paid to consul-

tants experience a much larger increase after the treatment than fees paid to auditors (from annual

AuditAnalytics). Moreover, when I divide treated banks based on whether their post-treatment 10-K

notes cite internal controls consulting as a component of professional expenditure, the increase in

professional expenditure is larger for treated banks that cite internal controls as a significant source

of expenditure.15

Managerial Rents

In this section I provide empirical support for the hypothesis that reduced monitoring costs increase

managerial rents, where I measure managerial rents by earnings smoothing (Fudenberg and Tirole

(1995)). Specifically, I use the August 2007 rise in money market interest rates as a shock to the

15In many banks, internal controls expenditures are related to Sarbanes-Oaxley (SOX). In the appendix, I show that theobserved decline in treated banks’ valuation is however not due to interactions between the policy and size-related SOXprovisions (see, for example, Iliev (2010)).


Table 1.5

Professional Expenditure Growth and Post-Treatment Value Losses

In this table I study the interaction between post-treatment professional expenditure growth and post-treatment bank value losses. In the table, the term “Post × Treated × Prof. Fees” captures treated banks’professional expenditures that only occur after the treatment. Z-Score is computed as the moving average ofbank capital-asset ratio (book value of equity divided by book value of assets), plus the moving average ofROA, divided by the moving standard deviation of ROA. Moving averages are calculated over a horizon ofthree quarters. Equity Volatility is the quarterly standard deviation of daily equity returns. Tail risk is thenegative of the average return over the 5% worst return days that a bank’s stock experiences in a given quar-ter (Ellul and Yerramilli (2013)). Professional fees are normalized by net interest income. Unreported controlvariables include total assets, leverage, profitability, ROE, diversification, and asset growth.


(1) (2) (3) (4) (5) (6)

Post × Treated -0.001 -0.001 -0.000 0.003 -0.000 0.004(0.01) (0.01) (0.01) (0.04) (0.03) (0.03)

Prof. Fees -0.037 -0.067 -0.075* -0.103 -0.244 -0.437(0.05) (0.04) (0.04) (0.52) (0.45) (0.36)

Post × Treated × Prof. Fees -0.139*** -0.105** -0.124** -1.447*** -1.196*** -1.188***(0.05) (0.05) (0.06) (0.54) (0.43) (0.39)

Z-Score 0.000 0.000 0.000 0.000(0.00) (0.00) (0.00) (0.00)

Equity Volatility 1.681*** 1.681*** 11.419*** 10.430***(0.29) (0.25) (1.41) (1.55)

Tail Risk -0.813*** -0.789*** -6.008*** -5.713***(0.11) (0.10) (0.63) (0.54)





funding costs of BHCs with total assets around $500 million, and analyze the impact of this negative

shock on managerial earnings smoothing right above and right below the threshold. Since money

market interest rates are determined in the interbank lending market of large banks, non-systemic

banks with assets around $500 million arguably play a negligible role in determining this funding

shock. Any observed difference in funding costs and earnings smoothing of banks right above and

below the threshold should therefore only arise from the different exposure of these banks to Fed

monitoring.

To test whether the 2007 shock has a different impact on banks with assets right above and right

below the threshold, I construct two new groups of treated and control BHCs. The new group of

treated, “unmonitored” BHCs consists of BHCs with less than $500 million in assets during the 2006-

2008 period. The new group of control, “monitored” BHCs consists of BHCs with more than $500

million in assets during the same period. To avoid potential bias due to the change in the definition

of small BHCs, I drop observations before the first quarter of 2006. Moreover, I drop BHCs with

total assets above $700 million such that systemic banks are excluded from the sample and such that

the unmonitored and monitored groups have roughly the same number of banks (sixty-seven and

fifty-seven, respectively). My results are not sensitive to this sample bandwidth choice.

In Table 1.6 I report my main results on the impact of Fed supervision on funding costs, profitability,

and earnings smoothing during the crisis.16 Panel A shows the impact of Fed supervision on the

funding costs and profitability of unmonitored banks relative to monitored banks. In the first two

specifications of Panel A, I use total interest expense divided by total loans as a measure of BHC

funding costs. The table shows that during the crisis the difference between the cost of funding of

unmonitored and monitored banks increases by 5.3 percent relative to the pre-crisis period, and that

this effect is robust to the inclusion of lagged Tobin’s q, leverage, Tier 1 Ratio, total assets, diver-

sification and asset growth as regression covariates. The next specifications show that this relative

increase in unmonitored bank funding costs is however not associated with an increase in interest

revenue (interest income divided by total loans), and only by a marginally significant decrease in

16Summary statistics for the dependent variables used in this section are reported in the appendix.


ROE. As a result, unmonitored banks’ higher funding costs must be followed by higher noninterest

revenue, lower noninterest expense, or both.

In the first two specifications of Panel B, I show that unmonitored bank Loan Loss Provisions—a

component of noninterest expense—indeed experience a large decline during the financial crisis.

While the results of the baseline Specification (1) are not statistically significant, the second specifica-

tion of Panel B shows that during the crisis unmonitored bank LLPs decrease by fifty-three percent

relative to monitored bank LLPs after controlling for size, profitability, and other sources of bank

heterogeneity. The observed decline is not due to bank size or performance, and is therefore consis-

tent with the hypothesis of earnings smoothing (as previously documented by Huizinga and Laeven

(2012)). In the last four specifications of Panel B, I confirm this hypothesis by showing a relative in-

crease in small bank Discretionary Negative Loan Loss Provisions (DNLLPs) during the crisis. These

discretionary provisions are the absolute negative residuals from a first-stage regression of LLP on

observable performance variables, and measure the negative change in LLP that is not due to bank

performance (Kanagaretnam, Lim, and Lobo (2014)). Panel B shows a relative DNLLPs increase as

large as seventy percent for unmonitored banks, confirming that the decline in LLP documented in

the first two specifications is due to managerial discretion as opposed to performance.

In the appendix, I conduct additional tests to address potential concerns that the results of Table 1.6

are driven by a subset of small, distressed banks during the crisis rather than by Fed monitoring. In

particular, I show that the results are robust within the sample of banks surviving for the entire 2006-

2008 period, and lose economic and statistical significance when I choose an alternative threshold of

$400 million to define the two groups of unmonitored and monitored banks.

Cash Flow Risk

In Table 1.7 I test my third prediction that banks with higher cash flow risk should experience a

larger decline in value and a larger increase in monitoring expenditure after the treatment. To do

so, I divide treated banks into two sub-groups based on whether their average cash flow risk (as

defined in Section 1.3.1) is above or below the median cash flow risk in my sample. In the table, I


Table 1.6

Managerial Rents: Earnings Smoothing in the Financial Crisis

In this table, I study the impact of Fed monitoring on bank funding costs, profitability, and earnings smoothingduring the financial crisis. In Panel A, I study the change in funding costs (total interest expense dividedby total loans), interest revenue (interest income divided by total loans), and ROE. In Panel B, I study thechange in LLP (loan loss provisions normalized by net interest income) and DNLLP (constructed followingKanagaretnam et al. (2014) as the absolute negative residual from a regression of LLP on previous-quarterloan loss allowance, current-quarter loan charge-offs to assets, loans to assets, non-performing loans to assetsand change in total loans) during the financial crisis. The dependent variable used to calculate DNLLP 1 iscurrent-quarter LLP, while the dependent variable used to calculate DNLLP 2 is previous-quarter LLP. Thesample period is 2006-2008. Unmonitored banks are banks that are below the $500 million threshold for theentire sample period. Unreported controls include previous-quarter Tobin’s q, leverage, the Tier 1 Ratio, totalassets, diversification and asset growth in Panel A, as well as operating profitability and ROE in Panel B.

Panel A: Funding Costs and Profitability

log Int. ExpenseTotal Loans log Int. Income

Total Loans ROE

(1) (2) (3) (4) (5) (6)

Crisis × Unmonitored 0.053** 0.053*** 0.018 0.019 -0.008 -0.003(0.02) (0.02) (0.01) (0.01) (0.01) (0.00)

Controls No Yes No Yes No Yes


Panel B: Loan Loss Provisions

log LLPNet Int. Income log DNLLP 1 log DNLLP 2

(1) (2) (3) (4) (5) (6)

Crisis × Unmonitored -0.359 -0.531*** 0.610** 0.614** 0.704*** 0.708***(0.25) (0.18) (0.25) (0.25) (0.24) (0.24)





then study the treatment effect on value and professional expenditure in these two cash flow risk

groups. The table shows that treated banks with high cash flow risk experience larger value losses

than treated banks with low cash flow risk. For example, the relative loss in Market-to-Book for

treated banks with high cash flow risk is twice as large as the average value loss in the main sample,

while the relative value loss for treated banks with low cash flow risk is not statistically different

from zero. Moreover, treated banks with high cash flow risk also experience a much larger increase

in monitoring expense than treated banks with low cash flow risk, again in line with the predictions

of the model. In the appendix, I finally show that most of the results of the table also hold when

using alternative risk measures such as Z-Scores and equity return volatility.

Table 1.7

Cash Flow Risk, Shareholder Value, and Professional Expenditures

In this table I study the treatment effect on value and professional expenditure for treated banks with above-and below-median cash flow risk, where cash flow risk is defined as in Table 1.1. Unreported control variablesinclude leverage, Tier 1 Ratio, total assets, profitability, ROE, diversification and asset growth.

log Tobin’s q log Market-to-Book log Prof. Fees

(1) (2) (3) (4) (5) (6)

Post × Treated × Low CF Risk 0.001 -0.003 -0.015 -0.021 0.101 0.202**(0.00) (0.01) (0.04) (0.04) (0.10) (0.10)

Post × Treated × High CF Risk -0.018*** -0.014*** -0.152*** -0.114*** 0.421*** 0.338***(0.01) (0.01) (0.04) (0.04) (0.12) (0.08)


Year-Quarter FE Yes Yes Yes Yes Yes YesBHC FE Yes Yes Yes Yes Yes YesR-Squared 0.373 0.434 0.436 0.525 0.135 0.271Observations 1,547 1,547 1,547 1,547 737 737


1.5.2 Regulatory Monitoring and Shareholder Free-Riding

I finally argue that increased shareholder monitoring costs increase their incentives to free-ride on

each other’s monitoring (Grossman and Hart (1980), Holmstrom (1982)). Consistent with the the pre-

dictions of Shleifer and Vishny (1986), I show that the presence of a large shareholder—the chairman

of the board of directors—helps mitigating this free-rider problem and increases bank value.


Table 1.8

Ownership, Management Monitoring, and Value

In this table I study the post-treatment interaction between bank ownership, professional expenditure, andvalue, immediately following the treatment. I first assign treated banks to two groups based on whether theirpre-treatment chairman ownership falls in the bottom two terciles (low-ownership) or in the top tercile (high-ownership) of the pre-treatment chairman ownership distribution in my sample. In the table, I then study howdifferent levels of pre-treatment chairman ownership interact with changes in post-treatment professional ex-penditure and value. Since the focus of the table is the short-term treatment effect on professional expenditureand value, my estimates only include data from 2005 and 2006. Quarterly bank ownership data comes fromS&P Capital IQ. Unreported control variables include total assets, leverage, the Tier 1 Ratio, profitability, ROE,diversification, and asset growth.

log Prof. Fees log Prof. FeesNet Int. Income log Market-to-Book

(1) (2) (3) (4) (5) (6)

Post × Treated × Low Chair Own. 0.167* 0.183* 0.188* 0.187* -0.079*** -0.077***(0.09) (0.09) (0.09) (0.10) (0.03) (0.03)

Post × Treated × High Chair Own. 0.521*** 0.512*** 0.416*** 0.477*** -0.028 -0.045*(0.07) (0.06) (0.11) (0.08) (0.05) (0.03)




In Table 1.8, I investigate how different levels of chairman ownership affect monitoring costs and

valuation immediately after the treatment.17 Similar to Table 1.7, I first divide treated banks in two

groups based on whether their pre-treatment ownership by the chairman falls in the bottom two

terciles or in the top tercile of the pre-treatment chairman ownership distribution in my sample. In

the table, I then study the professional spending and value losses in these two groups of banks. The

main objective of this table is to show the short-term treatment effect on professional expenditure

and value for banks with different levels of ownership, and the table therefore only reports results

for the years 2005 and 2006.

The first four specifications show that banks with low and high levels of chairman ownership re-

17Ownership data comes from S&P Capital IQ. The results presented in the table are qualitatively similar, althoughstatistically and economically weaker, for other categories of ownership such as institutional ownership. A possible expla-nation for this result is that the banks in my sample are relatively small compared to other financial institutions, and likelyrepresent a small fraction of institutional investors’ portfolio (Fich, Harford, and Tran (2015)).


spectively increase their professional expenditure by eighteen and fifty-one percent after the tre-

atment. In absolute terms, these relative changes translate into an average twenty-five thousand

dollar increase in professional expenditure for banks with low chairman ownership, and an average

thirty thousand dollar increase for banks with high chairman ownership. Despite the much larger

increase in relative professional expenditure and the slightly larger increase in absolute expenditure,

the last two specifications show that treated banks with high chairman ownership only experience

around sixty percent of the value drop of treated banks with low chairman ownership.18 In other

words, while the discounted present value of bank professional expenditure is approximately the

same across the two ownership groups, the valuation of banks with low chairman ownership drops

by much more than the valuation of banks with high chairman ownership.

Consistent with the idea that ownership resolves shareholder free-riding problems, in the appendix

I finally show that the treatment effect on professional expenditure is not only larger but also more

persistent in banks with high chairman ownership. At the same time, the post-treatment drop in

shareholder value is lower and less persistent for these banks relative to banks with low chairman

ownership.

1.6 Discussion and Tests of Alternative Hypotheses

Collectively, the results of the previous sections suggest that the large value losses of treated banks

are due to increased shareholder monitoring costs. Quantitiatively, the discounted present value of

increased monitoring expenditures accounts for around twenty-five percent of their loss in share-

holder value. Moreover, as just shown in Section 1.5.2, around forty precent of the value loss can

be attributed to free-riding problems as shareholder monitoring becomes more expensive. Follo-

wing the guidance of my model and my previous empirical results, I finally attribute the residual

shareholder value losses to increased managerial rents.

18Pre-treatment valuations in the two ownership groups are not statistically different from each other.

1.6. DISCUSSION AND TESTS OF ALTERNATIVE HYPOTHESES 33

Despite empirical evidence supporting the model’s predictions, my results make it difficult to fi-

nally conclude that the residual shareholder value losses are necessarily due to mangerial rents. My

strategy is to rule out alternative hypotheses that might explain these residual value losses.19

Government Tail Risk Insurance An important question is whether the government provides dif-

ferent degrees of tail risk insurance to small and large banks. If this is the case, part of the discounts

observed in treated bank value might just reflect a loss of government insurance, as opposed to re-

duced Fed monitoring. To test this hypothesis, I construct a daily version of the Gandhi and Lustig

(2015) risk factor capturing aggregate tail risk in US banks’ stock returns. As discussed in their paper,

this size factor is the normal risk-adjusted return on a portfolio that goes long in small bank stocks

and short in large bank stocks, and represents a bank-specific risk factor orthogonal to other equity

and bond factors. In the appendix, I test whether treated banks experience a change in their expo-

sure to bank-specific tail risk after the treatment, where I measure this risk exposure as the quarterly

loading of bank excess returns on the size factor. In practice, I repeat the usual exercise using each

bank’s quarterly loading on the size factor (the estimate from a quarterly time-series regression of

daily bank excess returns on the daily size factor) as dependent variable. My results show no sig-

nificant changes in deregulated banks’ exposure to tail risk, and therefore to government tail risk

insurance.

Financial Statement Disclosure A second possible channel for the residual losses in treated bank

value is reduced financial disclosure (Hutton et al. (2009)). To rule out this hypothesis, I use a policy

provision of the Fed policy allowing treated BHCs to keep filing form FR Y-9C, while also preventing

them to revert to form FR Y-9SP if they choose to do so. Following this provision, I define treated

banks as voluntary filers if they file form FR Y-9C in March 2006 (the first quarter in which the policy

becomes effective).20 In the appendix, I analyze the treatment effect on twenty-nine voluntary filers

19For expositional convenience, the tables relative to this section are confined to the appendix.20The policy gives the Fed the option to determine if a small bank should file form FR Y-9C based on additional indi-

vidual criteria such as diversification. However, this provision is only effective from the second half of 2006 and virtuallynever used by the Fed in subsequent periods.


(the voluntary-reporting group), and compare it to the effect on the remaining treated banks (the not-

reporting group). The treatment effect on each sub-group is a one percent decrease in Tobin’s q, both

in baseline specifications and when I add time-varying controls. Similarly, the treatment induces a

7.7 percent drop in voluntary-reporting BHCs’ Market-to-Book, almost identical to the 7.6 percent

drop for not-reporting BHCs. The results are similar when I add time-varying controls, confirming

that the treatment affects treated banks irrespective of their financial disclosure.

Liquidity, Volatility, and Market Frictions Another possible concern is that the stocks of treated

BHCs become riskier or less liquid following the treatment. Lower information availability might

decrease the liquidity of treated banks’ stocks—therefore justifying an illiquidity premium. Alter-

natively, institutional investors might treat the stocks of small and large banks differently, possibly

using Fed thresholds to define their investment strategy. For example, if many institutional inves-

tors can only hold stocks of large banks, one would expect a decrease in turnover, an increase in

idiosyncratic risk, and a decrease in market information responsiveness for treated banks’ stocks.

My results show no significant changes in the liquidity, volatility, and market information responsi-

veness of treated banks’ stocks after the treatment. More specifically, the data shows no significant

changes in five stock liquidity measures commonly used in the market microstructure literature, na-

mely Effective Tick Size (Holden (2009), Goyenko, Holden, and Trzcinka (2009)), the Corwin and

Schultz (2012) Bid-Ask Spread measure, the Amihud (2002) measure, Zero Days Traded (the number

of days in which a stock is not traded) and Turnover (traded volume divided by shares outstan-

ding). Similarly, the data shows no significant changes in treated banks’ risk profile, where I use

the standard deviation of BHC stock returns to measure total risk and the residual standard devia-

tions from the Fama-French four factor model and the Adrian, Friedman, and Muir (2015) Financial

CAPM model to measure bank idiosyncratic risk. Finally, I find no evidence of changes in stock price

responsiveness to market information, as measured by the delay variables of Hou and Moskowitz

(2005).

Leverage and Capital Requirements I finally analyze the treatment effect on leverage and capital

ratios. The policy closely follows another Fed regulation relaxing the capital requirements of treated

1.7. CONCLUSION 35

BHCs’ parent companies (71 FR 9897). According to this regulation, the parent companies of BHCs

with less than $500 million in total assets (i.e. the parent companies of treated BHCs) are exempted

from regular capital requirements to finance levered acquisitions. Although unlikely (capital requi-

rements exemptions are optional, and the banking subsidiaries of treated BHCs are still subject to

regular capital requirements), there might be a concern that high leverage increases bank default

risk, resulting in lower valuation. The appendix shows that the leverage and the regulatory capital

ratios of treated banks do not change after the treatment.

1.7 Conclusion

In this paper, I use a Fed policy relaxing the reporting requirements of a subset of US banks as a

quasi-natural experiment to investigate the impact of regulatory monitoring on shareholder value.

The paper shows that Tobin’s q and equity market-to-book of deregulated banks respectively fall by

one and seven percent after the policy, and shows that this result is due to an increase in shareholder

monitoring costs when regulatory monitoring decreases. I show that, absent regulatory monitoring,

increased shareholder monitoring costs lead to increased monitoring expenditure, managerial rents,

and free-riding problems between shareholders.

From an economic standpoint, the paper shows that monitoring has a large impact on firm value,

and demonstrates the positive role of regulation in reducing shareholder monitoring costs. From

a policy standpoint, the paper provides an empirical counter-argument to the standing view that

financial regulation is bad for bank investors, especially in small and medium-sized banks. In this

sense, future work should be aimed at measuring the contribution of agency frictions to the value

discounts observed in very large banks (Minton et al. (2017)), and quantifying the costs and benefits

of financial regulation for these large, complex financial institutions.

Chapter 2

Group Punishments without Commitment

37

38 CHAPTER 2. GROUP PUNISHMENTS WITHOUT COMMITMENT

2.1 Introduction

Teams exist in many economic settings, ranging from teams of individuals working together in clubs,

partnerships, or firms, to teams of companies in the form of cartels and lobby groups, to teams of

nations in the form of political alliances and economic unions. In each of these settings, teams aim

to improve outcomes by coordinating efforts across members and are often successful in doing so.

Organizing as a team, however, may also introduce moral hazard problems, especially when team

outcomes are shared and individual effort is not perfectly observed.

In static environments of team production subject to unobservable moral hazard, Holmstrom (1982)

shows the only way to alleviate moral hazard problems is to rely on an outsider who can punish

the entire team after observing an aggregate outcome associated with a deviation by some team

member. Punishments take the form of throwing away some share of the team’s output. Holmstrom

(1982) argues that the intervention of an outsider is also necessary to implement such punishments

in a repeated environment, as the team might not want to enforce these punishments once team

production outcomes are realized: “There is a problem [...] in enforcing such group penalties if they are

are self-imposed by the worker team. [...] Ex post it is not in the interest of any of the team members to waste

some of the outcome. But if it is expected that penalties will not be enforced, we are back in the situation with

budget-balancing, and the free-rider problem reappears.”

In this paper, we ask if and under what conditions outsiders are truly needed to enforce group

punishments in a repeated context. In other words, we ask whether the ability of individual team

members to punish other team members in the future enables the team to enforce group punishments

which occur after aggregate outcomes are realized but before the realization of individual payoffs in

the current period. We call such within-the-period punishments static group punishments. Since these

punishments occur sequentially after individuals choose their private actions, this environment re-

sembles a repeated extensive form game as in Mailath et al. (2017). We obtain a simple characteri-

zation of the set of public perfect equilibrium payoffs and show that, depending on the nature of

the payoffs that agents obtain from team production, the team can indeed enforce static group pu-

2.1. INTRODUCTION 39

nishments. In such cases, the threat of static group punishments is welfare enhancing relative to an

environment in which the team’s action set does not allow for static group punishments.

We start our analysis from a generalized model of repeated team production, featuring a team of

agents and a benevolent Principal—a construct to represent team-wide preferences. In our model,

agents individually choose a level of effort to contribute to the realization of a common outcome.

After observing this common outcome, the Principal chooses a group punishment (possibly zero)

which negatively affects the common outcome. The Principal, like the agents, cannot commit to

a long-term strategy for group punishments. Since the Principal’s action occurs after the common

outcome is observed, the benevolent Principal values period utility of all agents plus the sum of

future discounted stage-game payoffs of all the agents.

Our main contribution is to show that this commonly studied repeated team production environ-

ment admits a simple, recursive characterization for the set of perfect-public equilibria. Specifically,

we show how to characterize the entire equilibrium set of our generalized team production mo-

del using simple “carrot-and-stick” strategies for the worst perfect-public equilibrium (as in Abreu

(1986)). We show that group punishments reduce the gains from deviations in the “carrot” phase,

but increase the gains from deviations in the “stick” phase. Therefore, deviations from the “stick”

never call for immediate implementation of group punishments, further simplifying the recursive

characterization of the equilibrium set.1

Our main findings are that static group punishments can be enforced by the threat of future actions

by team members; and that the threat of static group punishments strictly improves the best attaina-

ble equilibrium welfare relative to an economy where the Principal’s actions are restricted to never

implement group punishments. Moreover, we show that a necessary condition for static group pu-

nishments to improve welfare is the presence of complementarities between aggregate outcomes

and private actions in team members’ stage game payoffs. We show that the total static deviation

payoff (the total payoff that a deviant team member obtains within the deviation period) can be ex-

pressed as the deviant’s static private gain minus a cost to incentivize the Principal to implement

1We argue that imperfect observability plays a key role in our recursive characterization, making continuation payoffsindependent of the identity of the deviator (Mailath et al. (2017)).


group punishments. Absent complementarities between aggregate outcomes and private actions,

group punishments have no impact on this total static deviation payoff, and are therefore ineffective

in deterring individual deviations—an outsider a la Holmstrom (1982) is required to improve wel-

fare. Conversely, when team members’ private actions interact with aggregate outcomes group pu-

nishments do reduce the total static deviation payoff by indirectly reducing team members’ private

incentives to deviate. In these cases, group punishments are useful to deter individual deviations,

and an outsider may not be needed to improve welfare.

Our findings in the generalized model indicate that in presence of complementarities between ag-

gregate outcomes and private actions, the Principal who lacks commitment (i.e. the team) might

be capable of replicating incentive schemes which do not satisfy budget balancing without the aid

of outsiders. In the second part of the paper, we apply our generalized team production model to

the repeated oligopoly model of Abreu (1986), and ask which features of producers’ payoffs make

self-imposed group punishments most effective in improving team welfare—and therefore limit the

need for an outsider. In the oligopoly model, team members are producers individually choosing

how much output to produce, and the team outcome is the common price faced by all producers (a

decreasing function of aggregate team output). On the other hand, the group punishment imposed

by the Principal is a tax rate (possibly zero) which has the effect of reducing the price of producers’

output. As in the generalized model, the Principal cannot commit to a long-term strategy for taxes.

Within the context of the oligopoly model, we first show that group punishments imposed by the

Principal are particularly effective in increasing team welfare for intermediate levels of the produ-

cers’ discount factor. Intuitively, when producers are very impatient the threat of future punishments

is weak and only small group punishments can be sustained following static deviations. For inter-

mediate levels of the discount factor, the team can sustain large enough static group punishments

such that the threat of these punishments allows the team to achieve the socially-optimal level of

production. When producers are very patient, the threat of future punishments is strong enough

that the team can sustain the socially-optimal level of production even without resorting to group

punishments. Second, we show that for a given level of the discount factor group punishments are


more effective when producers’ output is highly substitutable. In these cases, deviations by indi-

vidual producers have a small impact on the common price, increasing producers’ static incentives

to deviate, and increasing the ability of group punishments to improve team welfare relative to an

economy where group punishments are not part of the team’s action set.

Related Literature Our paper is related to a large literature concerning moral hazard in static team

production settings. Alchian and Demsetz (1972) describe the opportunity for team members to shirk

and still receive compensation and the need for a principal to prevent shirking. Holmstrom (1982)

suggests a particular kind of contract in which a principal withholds payment whenever output is

below its socially optimal level. Other studies solve the moral hazard problem by injecting a de-

gree of competition among team members via tournaments, rankings, or other relative performance

measures (see Hart and Holmstrom (1986) for a survey).

One of the main challenges in taking these static team production games to the infinitely-repeated

domain is to characterize the set of perfect-public equilibrium payoffs. Mailath et al. (2017) show

that in a wide range of extensive-form games (including team production games) the equilibrium

set cannot be characterized using simple penal codes, because both within-period punishments and

continuation payoffs need to fit the identity of the deviator after a deviation has occurred. In our

paper, we assume that group punishments can only affect team outcomes (due to imperfect observa-

bility), and show how under this assumption the equilibrium set can be characterized using simple

penal codes. In other words, we show that simple penal codes can be used to characterize the entire

set of perfect-public equilibrium payoffs in a broad set of repeated extensive-form games featuring

imperfect observability.

An alternative to group punishments is to allow agents to make side payments to each other (Goldlucke

and Kranz (2012, 2013)). This arrangement avoids costly forms of retaliation when an agent deviates,

and yet is still incentive-compatible since the non-deviant agent receives a positive money transfer

from the deviant. Harrington and Skrzypacz (2007, 2011) describe how the lysine and citric acid car-

tels successfully used these types of contracts, and employed monitors to audit the money-transfer


process. This class of models offer a recursive characterization of the equilibrium set using simple

penal codes, but is limited to teams of two agents or settings in which individual actions are obser-

vable.

More in general, our analysis is concerned with team production when a static game is repeated for

infinitely many periods. In this setting, agents have an opportunity to retaliate against the team in

future periods if shirking is detected (Fudenberg and Maskin, 1986; Ostrom et al., 1992). Moreo-

ver, in repeated settings enforcing the aforementioned mechanisms of peer evaluations and relative

performance rankings can become strategic problems in their own right, as exemplified by Che and

Yoo (2001), Fuchs (2007), and Cheng (2016). Finally, our question bears some similarity to the “Who

will guard the guardians?” question examined in Hurwicz (2008), Rahman (2012), Aldashev and

Zanarone (2017), and Acemoglu and Wolitzky (2015) among others. Our setup differs slightly in that

the guardian is the team itself, and individual team members must be willing to retaliate against the

team when group punishments are not enforced.

2.2 A Generalized Model of Repeated Team Production

We begin by describing a model of repeated team production where a benevolent Principal can im-

pose group punishments after observing aggregate deviations. We provide conditions under which

the Principal’s ability to impose static group punishments—defined as punishments that occur after

aggregate output is observed, but before currrent-period payoffs are realized—can be sustained in

equilibrium to increase the welfare of the team. Moreover, if team members are sufficiently patient,

the threat of these punishments can strictly increase team welfare relative to an environment where

the Principal’s actions are restricted to never implement group punishments.

2.2.1 Stage Game

A team consists of n agents indexed by i = 1, . . . , n.2 Each agent chooses an unobservable and non-

negative action ai ∈ R+, representing a level of effort. The cost of action ai is given by c(ai), where2In what follows, we use the terms “agents”and “team members” interchangeably.

2.2. A GENERALIZED MODEL OF REPEATED TEAM PRODUCTION 43

c′(ai) > 0, c′′(ai) ≥ 0, and c(0) = 0. Moreover, we write

a−i = (a1, . . . , ai−1, ai+1, . . . , an) , a = (ai, a−i) ,

where the vector a constitutes an effort profile. An effort profile determines the aggregate outcome of

team production according to a generic outcome function x : Rn+ → R+.

In addition to team members, a benevolent Principal (a construct for team payoffs) observes the

aggregate outcome x and chooses a group punishment τ ≥ 0 that reduces the team’s aggregate out-

come. A strategy for the Principal is therefore τ : R+ → R+. For notational convenience, we define

the final result of the team’s effort after the Principal imposes punishments as the aggregate net out-

come function `(a, τ), where ` : Rn+1+ → R+. We make two sets of assumptions on this aggregate

net outcome function. First, `τ(a, τ) < 0, where the subscript denotes the partial derivative of `(·)

with respect to τ. This assumption reflects the fact that in our model the Principal is just a construct

for the team. Since the only resource available to the Principal is the outcome of team production,

the Principal can never increase this outcome using group punishments. In other words, our first

assumption rules out external subsidies from the model. Second, to keep the analysis close to Holm-

strom (1982) we assume that for all i, j, ài (a, τ) = àj(a, τ) ≥ 0 and àiaj(a, τ) ≤ 0, where the subscripts

again denote partial derivatives.

Finally, the net outcome ` is distributed among team members according to a predetermined set of

sharing rules {si}ni=1, where each si ∈ (0, 1) and

n

∑i=1

si = 1. (2.1)

To keep our analysis concise, we limit ourselves to cases where si = 1/n. This assumption can be

relaxed to other sharing rules as long as each si is constant and (2.1) is satisfied.

Team members have identical preferences over their share of the aggregate outcome. Utility is given

by π : R+ → R which satisfies standard assumptions π′(`) > 0, π′′(`) ≤ 0, and lim`→0 π(`) = −∞.

Additionally, utility from output interacts with individual effort according to a function f : R+ →

R+, which satisfies f ′(ai) ≤ 0 and f ′′(ai) ≤ 0. The function f (·) represents possible interactions


between the common payoff component, `(a, τ), and the individual agent’s private effort ai, and

its interaction with π (·) allows us to nest the Abreu (1986) repeated oligopoly model within our

generalized framework. In the oligopoly model, π (·) and f (·) respectively correspond to prices and

quantities. Prices, like output shares, are common across all agents. Quantities, however, can vary

across agents.3 In our more general setting, one interpretation sees f (·) as part of a labor/leisure

trade-off, while the cost function c(·) reflects all other personal costs related to production. The

important feature that f (·) captures is that private and public gains from effort have a nontrivial

interaction. In this general model, we can discipline this interaction more explicitly through our

assumptions on f (·). Later on, we remove this interaction and find that a principal has no ability to

improve outcomes.4

Since the Principal ignores sunk effort costs c(·), payoffs to the agents and Principal are respectively

u(ai, a−i, τ) = π(si`(ai, a−i, τ)) f (ai)− c(ai), (2.2)

w(a, τ) =n

∑i=1

π(si`(a, τ)) f (ai). (2.3)

Stage Game Equilibrium

A symmetric perfect-public equilibrium of the stage game consists of effort choices ai by team members

and a group punishment choice τ(x) by the Principal such that for every x, τ(x) maximizes (2.3) and

such that given τ and a−i, ai maximizes (2.2)

Since in a static setting it is optimal for the principal not to impose group punishments (i.e. to set

τ(x) = 0), the optimal effort aN of the static equilibrium, which we denote by aN , is given by

aNi = argmaxai

[π(si`(ai, aN

−i, 0)) f (ai)− c(ai)]

. (2.4)

3The fact that oligopoly prices decrease in q while output shares increase in a is offset by f (a) decreasing in a while q isincreasing (in itself).

4The assumption that lim`→0 π(`) = −∞ is only needed when ài ≥ 0 to ensure that the team members can imposeunbounded punishments on each other. On the other hand, the assumption that f ′(·) ≤ 0 is necessary to guarantee theproblem has an interior solution when ài ≥ 0. More generally, the necessary assumption for the repeated model of teamproduction to have an interior solution is that sign(ài ) = −sign( f ′). The assumption that f ′′(·) ≤ 0 is sufficient but notnecessary to obtain our results, and allows us to easily compare the generalized model with the repeated oligopoly modelof Abreu (1986) in Section 2.3.


Note that facing the Principal’s optimal decision not to impose group punishments, the socially-

optimal level of effort a∗ which maximizes the sum of individual utilities is given by

a∗ = argmaxa

n

∑i=1

u(ai, a−i, 0). (2.5)

In the following Lemma 2.2.1, we establish that the equilibrium level of effort of this static game is

smaller than the socially-optimal level of effort.

Lemma 1. 0 < aNi < a∗i .

Proof. An individual agent’s first-order conditions yield

siài (ai, a−i, 0)π′(si`(ai, a−i, 0)) f (ai) + f ′(ai)π(si`(ai, a−i, 0)) = c′(ai). (2.6)

The profile aN necessarily satisfies (2.6) for all agents i = 1, . . . , n. That is,

siài (aN , 0)π′(si`(aN , 0)) f (aN

i ) + f ′(aNi )π(si`(aN , 0)) = c′(aN

i ). (2.7)

The first order condition for the socially-optimal level of effort, on the other hand, implies that for

all i

sià(a∗, 0)π′(si`(a∗, 0)) f (a∗i ) + f ′(a∗i )π(si`(a∗, 0)) + ∑j 6=i

sjài (a∗, 0)π′(sj`(a∗, 0)) f (a∗j ) = c′(a∗i ). (2.8)

Conditions (2.6) and (2.8) differ by an additional term in (2.8). This extra term represents the positive

externality of one agent’s additional effort on the remaining (n− 1) agents. Since π′ > 0, si ∈ [0, 1],

and f (aj) > 0 for any aj > 0, the additional term is necessarily positive. This implies that


i ) + f ′(aNi )π(si`(aN , 0))− c′(aN

i ) >

siài (a∗, 0)π′(si`(a∗, 0)) f (a∗i ) + f ′(a∗i )π(si`(a∗, 0))− c′(a∗i ). (2.9)

The result follows from our assumptions on `(·), π(·), and f (·). Since lim`→0+ π(`) = −∞, we rule out

the boundary solution aNi = 0, so 0 < aN

i < a∗i .


Note that if the Principal were able to commit to group punishments when the aggregate outcome

is smaller than x(a∗), then each producer contributing a∗i would be an equilibrium. For example,

for a given effort profile a, if the Principal’s strategy was to implement some τ (x (a)) > 0 such that

`(a, τ (x (a))) = 0 if x(a) < x(a∗), and conversely to implement τ = 0 if x(a) = x(a∗), then each agent’s

best response to a∗−i would be to choose ai = a∗i .5 In this sense, the threat of group punishments

would be useful if the Principal could commit to such a strategy. In the next section, we investigate

whether group punishments may be sustainable and welfare-improving when agents and the Princi-

pal interact repeatedly. Before proceeding to the repeated game, we establish the intermediate result

that agents will increase their effort in the interior of [aNi , a∗i ] when a−i < aN

i .

Corollary 2. If a−i < aNi , then the most profitable deviation a′i is such that a′i > aN

i .

Proof. Consider the condition that is satisfied when ai = aNi for i = 1, . . . , n.


i ) + f ′(aNi )π(si`(aN , 0)) = c′(aN

i ). (2.10)

Now suppose that the effort by all other producers but i (denoted by a−i) decreases from aNi . Then,

si`ai (aNi , a−i, 0)π′(si`(aN

i , a−i, 0)) f (aNi ) + f ′(aN

i )π(si`(aNi , a−i, 0)) > c′(aN

i ). (2.11)

The optimal response a′i by agent must satisfy the first-order condition

si`ai (a′i , a−i, 0)π′(si`(a′i , a−i, 0)) f (a′i) + f ′(a′i)π(si`(a′i , a−i, 0)) = c′(a′i), (2.12)

which means that the right-hand side of (2.11) must increase and/or its left-hand side must decrease.

Therefore, a′i > aNi .

2.2.2 Infinitely-Repeated Game

In this section, we develop and analyze an infinitely-repeated version of the static team production

model described above. We focus on symmetric, perfect-public equilibria and illustrate how team

5In this example, we assume that for each a, there always exists some τ (x (a)) > 0 such that `(a, τ (x (a))) = 0. In otherwords, we assume that there exists a punishment such that the Principal can completely destroy the aggregate outcome.


members may incentivize the Principal such that group punishments are sustainable in equilibrium

even when the Principal lacks commitment. We go on to show that along the best equilibrium path,

group punishments are not implemented. However, the threat of group punishments allows team

members to attain strictly higher welfare than they would in an economy where group punishments

are not allowed—the Principal’s actions are restricted to never impose group punishments.

Histories, Perfect-Public Equilibria, and One-Shot Deviations

Here we describe the infinitely-repeated game, define our notion of equilibrium, and simplify our

equilibrium characterization by appealing to the one-shot deviation principle. Proposition 3 of this

section shows that the entire set of perfect-public equilibria can be attained by preventing single-

period (one-shot) deviations in the infinitely-repeated game.

Let hwt ∈ Hw where Hw = R2

+ denote the public outcomes (xt, τt) observed at the end of period t.

Then, letHw denote set of public histories withHw=⋃∞

t=0 (Hw)t. Similarly, define the set of histories

for agent i as Hi=⋃∞

t=0 (R+ × Hw)t. A pure strategy for agent i is a mapping from the set of all

possible agent i histories into the set of pure actions,

σi : Hi → R+.

A pure strategy for the Principal is a mapping from the set of public histories and an observation of

the aggregate outcome into the set of pure actions for the Principal,

σw : Hw ×R+ → R+.

We assume agents and the Principal have a common discount factor δ and restrict attention to public

strategies which are functions only of the public history. Given a strategy profile σ =({σi}n

i=1 , σw)

, if

hwt ∈ Hwt denotes a generic period-t history, we let Uti(hwt, σ

)denote the discounted continuation

payoffs agent i obtains from period t onwards. Since the Principal chooses an action after period-t


effort decisions are sunk, the Principal’s discounted continuation payoffs satisfy

Uwt(hwt, σ

)= ∑

iUi

t(hwt, σ

)+ (1− δ) c ∑

iσi(hwt) . (2.13)

In Appendix B.2.1 we define continuation games and strategies, perfect-public equilibria, and one-

shot deviations. In the next proposition, we prove that equilibria can be constructed recursively by

ensuring that for any history, neither the agents nor the Principal have a profitable one-shot devia-

tion.

Proposition 3. A strategy profile σ =({σi}n

i=1 , σw)

is perfect-public if and only if there are no profitable

one-shot deviations for the agents and there are no profitable one-shot deviations for the Principal.

Proof. See Appendix B.2.1.

Equilibrium Set Characterization

We now describe a procedure to characterize the set of symmetric equilibrium payoffs using carrot-

and-stick strategies as in Abreu (1986). As we will argue, individual deviations by team members

may be subject to group punishments chosen by the Principal. However, limited commitment of the

Principal implies that agents will need to impose discipline on the Principal in the event that the

Principal attempts to avoid the static losses associated with group punishments. Nonetheless, we

will show that extremal equilibrium payoffs (both the best and the worst equilibrium payoff) need

not feature group punishments.

We focus on characterizing strongly symmetric equilibria, and we therefore simplify our notation by

dropping i subscripts and by using a in place of (a, a, . . . , a) for producers’ strategies, u (a, 0) in place

of ui (a, a, . . . , a, τ = 0) for producers’ payoffs and so on.

Under the one-shot deviation principle, given the worst perfect-public equilibrium payoff v, the best

perfect-public equilibrium payoff v can be constructed as the solution to the following program:

v = maxa,τ(·),v(·,a,τ(·))

u (a, 0) , (2.14)


subject to, for all a′

u (a, 0) ≥ (1− δ) u(a′, a, τ

(x(a′, a

)))+ δv

(a′, a, τ

(x(a′, a

)))(2.15)

v(a′, a, τ

(x(a′, a

)))∈ [v, v] , (2.16)

and

(1− δ)w(a′, a, τ

(x(a′, a

)))+ nδv

(a′, a, τ

(x(a′, a

)))≥ (1− δ)w

(a′, a, 0

)+ nδv. (2.17)

Inequality (2.15) represents the incentive compatibility constraint for each agent, which requires the

symmetric payoff u (a, 0) to be greater or equal to the payoff associated with a deviation effort a′ with

static payoff u(a′, a, τ(x(a′, a))) and continuation payoff v(a′, a, τ(x(a′, a)). Equation (2.16) represents

the feasibility constraint for the continuation payoff v(a′, a, τ(x(a′, a)), which must lie between the

worst equilibrium payoff v and the best equilibrium payoff v. Finally, (2.17) is the incentive compa-

tibility constraint for the Principal, requiring the Principal to have sufficient incentives to enforce the

prescribed group punishment once one of the n team members deviates to a′. The left-hand side of

(2.17) is the Principal’s payoff when implementing the prescribed group punishment while the right-

hand side is the payoff from a deviation to τ = 0, followed by the worst perfect-public equilibrium

payoff v.

It is useful here to reduce the dimensionality of the problem by eliminating the Principal’s incentive-

compatibility constraint. Since (2.17) must bind in any solution to the above program, the continua-

tion payoff following a deviation by an agent must satisfy

v(a′, a, τ

(x(a′, a

)))= v +

1− δ

δ

1n[w(a′, a, 0

)− w

(a′, a, τ

(x(a′, a

)))]. (2.18)

Hence, for any deviation a′, we may write the agent’s incentive-compatibility constraint (2.15) as

u(a′, a, 0

)≥ (1− δ)

[u(a′, a, τ

(x(a′, a

)))+

1n[w(a′, a, 0

)− w

(a′, a, τ

(x(a′, a

)))]]+ δv. (2.19)

Let g (a′, a, τ (x (a′, a))) denote the static payoff for an individual agent exerting effort a′ when all

other producers producers produce a—the term in the outer square brackets on the right-hand side


of (2.19). We call this quantity the total static deviation payoff. Using this definition, we re-write the

problem (2.14)-(2.17) as

v = maxa

u (a, 0) , (2.20)

subject to, for all a′,

u (a, 0) ≥ (1− δ) g(a′, a, τ

(x(a′, a)

))+ δv, (2.21)

v ≥ 1− δ

δ

1n[w(a′, a, 0

)− w

(a′, a, τ

(x(a′, a)

))]+ v, (2.22)

g(a′, a, τ

(x(a′, a)

))= u

(a′, a, τ

(x(a′, a)

))+

1n[w(a′, a, 0

)− w

(a′, a, τ

(x(a′, a)

))]. (2.23)

Note from (2.23) that the total static deviation payoff comprises two components. The first com-

ponent, u (a′, a, τ (x(a′, a))), represents the agent’s static utility from a deviation to a′ (under the

expectation that the Principal will implement the prescribed group punishment). The second com-

ponent, [w (a′, a, 0)− w (a′, a, τ (x(a′, a)))] /n, represents the deviating agent’s share of the net benefit

the Principal generates by deviating and not implementing the prescribed group punishment. Next,

it is useful to define the maximum deviation payoff an agent can achieve by deviating to a′ from

profile a, which we denote by g (a, τ (·)). This payoff satisfies

g (a, τ (·)) = maxa′

g(a′, a, τ(x(a′, a)

).

In the next lemma, we show that as long as the prescribed level of effort is smaller than the static

Nash equilibrium level of effort, the maximum deviation payoff g(a, τ (·)) is minimized when the

Principal imposes no group punishments (i.e. when τ = 0).

Lemma 4. Supppose that f ′(a) < 0. Then g (a, τ (·)) ≥ g (a, τ = 0) when a ≤ aN .

Proof. For notational simplicity, we remove the dependency of τ(·) on its arguments. Note that

∂g∂τ

= si`τ(a′, a, τ)π′(si`(a′, a, τ)) f (a′)

− 1n

si`τ(a′, a, τ)π′(sih(a′, a, , τ))[(n− 1) f (a) + f (a′)

](2.24)

= si`τ(a′, a, τ)π′(si`(a′, a, τ))n− 1

n[

f (a′)− f (a)]

. (2.25)


Since `τ ≤ 0 and π′ > 0, for ∂g/∂τ > 0 we need only show that [ f (a′)− f (a)] < 0. Since a ≤ aN ,

the most profitable deviation from a satisfies a′ > a by Corollary 2. As f (a) is decreasing, the most

profitable deviation satisfies f (a′) < f (a), which yields the desired result.

Lemma 4 establishes that group punishments (τ (·) > 0) increase the incentives of individual agents

to deviate when a ≤ aN . The first line of (2.24) reveals that a small increase in τ decreases total

output, in turn decreasing the total static deviation payoff. Intuitively, imposing punishments after

agents exert more effort reduces their incentives to do so. However, the second line of (2.24) reveals

that a small increase in τ may reduce the total static deviation payoff. The reason is that an increase

in τ increases in Principal’s incentive to deviate from implementing the group punishment. In sum,

(2.25) reveals that when f (a) is decreasing, the effect on the Principal’s incentives dominates the

effect on the agent’s incentives so that an increase in τ increases the total static deviation payoff

(when a ≤ aN). Imposing group punishments for excess effort in this region, therefore, strengthens

individual agents’ incentives to exert effort, and so has no use in enforcing the prescribed behavior.

Lemma 4 plays a key role in allowing us to characterize simple equilibrium strategies which obtain

the the infimum perfect-public equilibrium payoff v. To construct v, we propose a carrot-and-stick

strategy, which with a small abuse of notation we write as σ ((a, a) , (0, 0)). This strategy calls for

agents to play some “stick” level of effort a and subsequently revert to the “carrot” level a—the

level of effort prescribed in the best perfect-public equilibrium. If either the carrot or the stick are

played by all agents as prescribed by the strategy, the Principal chooses τ = 0. If the Principal

detects an aggregate deviation x(a′, a) 6= x(a) from the carrot a, the Principal chooses to implement

a group punishment τ(x(a′, a)) > 0, and the agents consequently revert to some strategy with value

v(a′, a, τ(x(a′, a)). If the Principal observes an aggregate deviation x(a′, a) 6= x(a) from the stick a,

the Principal chooses τ(x(a′, a)) = 0, and the producers consequently revert to the carrot-and-stick

strategy σ ((a, a) , (0, 0)) with value v. Finally, any deviation by the Principal causes the carrot-and-

stick strategy to be repeated.

Proposition 5. There exists an output a such that the carrot-and-stick strategy σ ((a, a) , (0, 0)) attains the

value v—that is, σ ((a, a) , (0, 0)) is an optimal punishment.


Proof. Given v, the infimum of symmetric perfect-public equilibrium payoffs and hence a (the value

that attains the maximum, v in the program (2.20)-(2.23)), we may obtain a such that

v = (1− δ) u (a, 0) + δu (a, 0) . (2.26)

We now argue that the carrot-and-stick strategy σ ((a, a) , (0, 0)) is an equilibrium. By construction,

the punishment has value v. Since deviations from a are unprofitable when punished by v, they are

by construction unprofitable when punished by σ ((a, a) , (0, 0)).

To show that no producer wishes to deviate when prescribed to contribute effort a, we must show

that for all a′,

v = (1− δ) u (a, 0) + δu (a, 0) ≥ (1− δ) g(a′, a, 0

)+ δv, (2.27)

and in particular

v = (1− δ) u (a, 0) + δu (a, 0) ≥ (1− δ) g (a, 0) + δv. (2.28)

We proceed by contradiction. Suppose (2.28) does not hold. Then there must exist another (strongly

symmetric) equilibrium σy with first-period output ay ≤ aN such that

(1− δ) g (a, 0) + δv > (1− δ) u (ay, 0) + δU (σy|ay) ≥ v (2.29)

where U (σy|ay) is the continuation payoff to a single producer from σy after contributing ay in the

first period.6

Replacing the definition of v in (2.29) implies

(1− δ) u (ay, 0) + δU (σy|ay) ≥ (1− δ) u (a, 0) + δu (a, 0) . (2.30)

6Since repeated play of the static Nash equilibrium output aN with no punishments must be an equilibrium, it isstraightforward to show that the prescribed effort under the “stick” must satisfy a ≤ aN . If ay > aN , however, (2.29)implies that

g(a, 0) > g(aN , 0).

Since the best deviation payoff in the absence of punishments is increasing in a, this would imply aN < a, a contradiction.


Since U (σy|ay) ≤ u (a, 0), it must be that u (ay, 0) ≥ u (a, 0) and therefore ay ≥ a. However, we will

show that if σy is a perfect-public equilibrium, a > ay, yielding the necessary contradiction. Since σy

is an equilibrium,

(1− δ) u (ay, 0) + δU (σy|ay) ≥ (1− δ) g (ay, τ (x(ay))) + δv, (2.31)

so that from (2.29)

(1− δ) g (a, 0) + δv > (1− δ) g (ay, τ (x(ay))) + δv. (2.32)

Since ay ≤ aN , Lemma 4 implies that

g (ay, τ (y(ay))) ≥ g (ay, 0) (2.33)

so that

g (a, 0) > g (ay, 0) . (2.34)

Since g (a, 0) is increasing in a, (2.34) implies a > ay providing the needed contradiction.

Proposition 5 greatly simplifies the characterization of the set of perfect-public equilibrium payoffs.

We have shown that the worst equilibrium payoff can be attained without requiring group pu-

nishments (either on the equilibrium path, or off the equilibrium path following deviations from

the “stick”). The key feature of our economy which yields this result is the fact that during the

“stick” phase of the worst equilibrium strategy, group punishments actually make deviations from

the stick more appealing to producers. Consequently the optimal strategy for the Principal is to not

impose group punishments. Using the results from Proposition 5, we now characterize strategies

that allow us to attain the entire set of perfect-public equilibria.

Proposition 6. If the strategy σ is a Perfect-Public Equilibrium, then u (σ) ∈ [v, v]. If v ∈ [v, v], then there

exists a Perfect-Public Equilibrium strategy σ such that u (σ) = v.

Here we provide a sketch of the argument and leave a formal proof to Appendix B.2.1. It is clear

that any equilibrium satisfies the constraints of the program (2.14)-(2.17) and therefore U(σ) ∈ [v, v].


It only remains to show that any value in this set may be attained by some equilibrium strategy.

We prove this result using an induction argument. To begin, it is straightforward to characterize

the set of values that can be attained with strategies which restrict the Principal never to impose

punishments (either on or off the equilibrium path). This set, which we denote [vA, vA] defines the

set of values that are attainable as subgame-perfect equilibria, and can be easily constructed with

carrot-and-stick strategies following Abreu (1986).

Since vA < vA, it is feasible to sustain one period of punishments in the event some agent deviates

from a prescribed level of effort. We therefore construct equilibria in which all agents are asked to

contribute some effort level a. If all agents do so, then no punishments are implemented and the

strategy repeats. If some agent deviates to some a′—so that the aggregate outcome is different than

x (a)—then the Principal is called upon to implement a punishment. If the Principal implements

the prescribed punishment, agents play some equilibrium without punishments which delivers the

value v(a′, a, τ). If the Principal does not implement the prescribed punishment, agents play the stra-

tegy associated with the worst equilibrium of a model where punishments are not allowed, with va-

lue vA. We choose a positive but sufficiently small punishment τ to ensure that v(a′, a, τ) ∈(vA, vA]

for all relevant deviations a′. We show that this strategy delivers equilibrium values u(a) > vA. Gi-

ven these strategies, we are able to construct carrot-and-stick equilibrium strategies which deliver

values strictly below vA. In following these steps, we have constructed an operator which maps

equilibrium value sets supported by perfect-public equilibrium strategies into similar sets that are

strictly larger and yet still attainable with perfect-public equilibrium strategies. We show that repe-

ated application of this operator starting from a set where group punishments are not part of the

Principal’s action set necessarily converges to the set [v, v] defined by the program (2.14)-(2.17). In

this way, we construct a perfect-public equilibrium strategy which delivers each value v ∈ [v, v].

We now use Proposition 7 to fully characterize the values of the best and worst perfect-public equi-

librium payoffs.


Proposition 7. The optimal carrot-and-stick punishment satisfies

g (a, 0) = (1− δ) u (a, 0) + δu (a, 0) = v, (2.35)

g (a, τ (·)) = u (a, 0) + δ (u (a, 0)− u (a, 0)) if a < a∗, (2.36)

and

g (a, τ (·)) ≤ u (a, 0) + δ (u (a, 0)− u (a, 0)) if a = a∗. (2.37)

The proof is a straightforward extension of those found in Abreu (1986) and hence relegated to the

Appendix (see Section B.2.1). Propositions 5 and 7 show that neither the best nor the worst perfect-

public equilibria feature group punishments imposed by the Principal. Nonetheless, we will show

momentarily that the out-of-equilibrium threat of group punishments allows team members to attain

higher welfare than in an economy where group punishments are not part of the Principal’s action

set. For expositional brevity, we will refer to such economy as an economy where group punishments

“are not allowed”. Let aA and aA respectively denote the carrot and stick levels of output in the

model where group punishments are not allowed. Similarly, let vA and vA denote the best and

worst perfect-public equilibrium values in the model where group punishments are not allowed.

Proposition 8 formally establishes that if the equilibrium output level a is sustained by a positive

punishment threat (a deviation by an agent is followed by a strictly positive group punishment

implemented by the Principal), then the presence of such a threat strictly improves welfare, or v > vA.

Proposition 8. For any equilibrium output levels a ≤ a∗, aA < a if a is sustained by a positive punishment

threat (for some a′ 6= a, τ (x (a′, a)) > 0), then v = u (a, 0) > u(aA, 0

)= vA.

Proof. First, note that since the Principal can always choose τ = 0,[vA, vA] ⊆ [v, v]. Therefore

u (a, 0) ≥ u(aA, 0

), or a ≥ aA. Now suppose by contradiction that if a is sustained by a positive

threat τ > 0, then a = aA. Since a = aA > aN , g(aA, 0

)= g (a, 0) > g (a, τ). From (2.36),

u(

aA, 0)

+ δ(

u(

aA, 0)− u

(aA, 0

))> u (a, 0) + δ (u (a, 0)− u (a, 0)) , (2.38)


or

u (a, 0) > u(

aA, 0)

. (2.39)

But from (2.35), this implies

v = (1− δ) u (a, 0) + δu (a, 0) > (1− δ) u(

aA, 0)

+ δu(

aA, 0)

= vA, (2.40)

a contradiction with[vA, vA] ⊆ [v, v].

We conclude this section by providing conditions on agents’ static payoffs such that group pu-

nishments improve welfare. Specifically, we note that the assumption underlying our Lemma 4

and Propositions 5 to 8 is that the private utility component f (ai), is decreasing in effort. Proposition

9 considers the alternative case where f (ai) is constant. We find that the interaction between pri-

vate and publicly observed payoffs is essential in enabling static group punishments to enlarge the

equilibrium set, relative to an economy where punishments are not allowed.

Proposition 9. Let κ be some constant. If f (a) = κ, for all a ∈ [0, a∗], static group punishments do not

improve equilibrium outcomes relative to a model where the Principal is not allowed to impose group pu-

nishments.

Proof. This result is clear from Equation (2.25). If f (a) = f (a′) = κ, then ∂g/∂τ = 0 and group pu-

nishment have no effect on producers’ payoffs.

Proposition 9 states that a necessary condition for static group punishments to improve welfare is

the presence of complementarities between aggregate outcomes and private actions in the individual

agents’ stage game payoffs. Absent these complementarities (i.e. when f (a) = κ), group punishments

have no effect on the total deviation payoff g because the impact of the punishment on the static

deviation gain u (a′, a, τ (x(a′, a))) is the exactly equal to the impact that these punishments have on

the per-capita share of the cost to incentivize the Principal, [w (a′, a, τ (x(a′, a)))− w (a′, a, 0)] /n.

2.3. AN APPLICATION: REPEATED OLIGOPOLY WITH A PRINCIPAL 57

When team members’ private actions instead interact with aggregate outcomes (i.e. f (a) is not con-

stant in a), then group punishments can reduce team members’ private incentives to deviate through

the interaction of these private incentives with the aggregate outcome. In these cases, group pu-

nishments are useful to deter individual deviations, and an outsider is not needed to improve wel-

fare. In other words, in presence of complementarities between aggregate and individual outcomes,

the team (represented by the Principal) can implement budget-breaking static punishments that im-

prove welfare without requiring the intervention of an outsider.

2.3 An Application: Repeated Oligopoly with a Principal

In this section, we apply our generalized team production model to the repeated oligopoly model

of Abreu (1986). We start by characterizing the stage game payoffs and equilibria, and we then

provide a numerical illustration of our main result that group punishments increase team welfare in a

repeated setting. In Section 2.3.3, we show how different degrees of interaction between oligopolistic

producers can impact the effectiveness of group punishments.

2.3.1 Stage Game

A team is composed by n producers indexed by i = 1, . . . , n. Each producer chooses an unobserva-

ble action qi ∈ R+ where qi represents a level of output generated by producer i. Each producer

generates output at a constant marginal cost c ∈ (0, 1). We let q = (q1, . . . , qn) ∈ Rn+ and we write

q−i = (q1, . . . , qi−1, qi+1, . . . , qn) , q = (qi, q−i) .

The producers’ choices of output give rise to an aggregate quantity of output Q = ∑ni=1 qi. Each

producer’s stage-game strategy is simply qi ∈ Rn+.

In addition to the producers, a benevolent Principal observes aggregate output Q and imposes an

observable group punishment τ ∈ [0, 1], which represents an implicit tax imposed by the Principal

on the consumers of the good. A strategy for the Principal is τ : R+ → [0, 1].


The price at which producers sell their output is a function of aggregate output and the tax chosen

by the Principal. Specifically,

p (Q, τ) = max {(1− τ)−Q, 0} . (2.41)

This price function represents an inverse demand curve for consumers who face taxes τ on purchases

of units of output. From (2.41) it is clear that the Principal’s choice of the tax may reduce the price of

output for all producers.

Given actions by the producers and the Principal, each producer’s payoff is given by

ui(q, τ) = p (Q, τ) qi − cqi. (2.42)

We again assume that the Principal is benevolent in the sense that the Principal has preferences over

a weighted average of the producers’ utility. Since the Principal chooses the tax τ after production

costs are sunk, the Principal’s payoff from any level of total output Q and tax τ is given by

w(Q, τ) = p (Q, τ) Q. (2.43)

Note that (2.42)-(2.43) immediately map to the generalized payoffs (2.2)-(2.3) when we i) impose

symmetric sharing rules (i.e. si = 1/n), ii) impose linear utility, interaction and cost functions of the

form π(si`) = si`, f (ai) = ai and c(ai) = cai, respectively, and iii) define the aggregate net outcome

function as `(a, τ) = n max{1− τ −∑i ai, 0}.7

A symmetric perfect-public equilibrium in the stage game consists of choices for producers qi and a

Principal’s strategy τ (Q) such that for every Q, τ (Q) maximizes (2.43) and given τ and q−i, qi

maximizes (2.42). This equilibrium is straightforward to determine since for any Q, the Principal

optimally chooses τ(Q) = 0. Facing q−i each producer’s best response satisfies

qi =

12 (1−∑−i q−i − c) if 1−∑−i q−i − c > 0,

0 otherwise,(2.44)

7Contrary to our generalized model, the oligopoly model’s net outcome function is such that, for all i, j, `ai (a, τ) =`aj (a, τ) < 0. This changes the sign of the main inequalities of our paper (for example, the Nash equilibrium level ofoutput is larger than the socially-optimal level of output), but the procedure to characterize the set of equilibrium payoffsis identical to the procedure developed in the previous section.


with the equilibrium level of qi satisfying

qNi =

1− cn + 1

. (2.45)

Note that facing the Principal’s optimal decision to set the tax equal to zero, the level of output which

maximizes the producers’ joint profits satisfies

qmi = arg max

qiqi (1− nqi − c) , (2.46)

with solution

qmi =

1− c2n

. (2.47)

From (2.45) and (2.47), observe that the level of output which maximizes joint producer profits is

lower than the perfect-public equilibrium outcome. Intuitively, producer i has an incentive to gene-

rate more output when the other producers generate less than qNi and prices are high. In contrast,

producer i has an incentive to generate less output when the other producers generate more than qN .

2.3.2 Infinitely-Repeated Game

As in the previous sections, we focus on characterizing strongly symmetric equilibria. Following the

same steps as in Section 2.2.2, it is easy to show that the generalized program (2.20)-(2.23) maps to

the following program in the repeated oligopoly model:

v = maxq

u (q, 0) , (2.48)

subject to, for all q′,

u (q, 0) ≥ (1− δ) g(q′, q, τ

(q′ + (n− 1) q

))+ δv, (2.49)

v ≥ 1− δ

δ

1n[w(q′ + (n− 1) q, 0

)− w

(q′ + (n− 1) q, τ

(q′ + (n− 1) q

))]+ v, (2.50)

where v and v again denote the worst and the best perfect-public equilibrium payoffs of the repeated

game, and where (using (2.42) and (2.43)) the total static deviation payoff g (q′, q, τ (q′ + (n− 1) q))


is given in closed-form by

g(q′, q, τ

(q′ + (n− 1) q

))= q′

((1− τ

(q′ + (n− 1) q

))−(q′ + (n− 1) q

)− c)

+1n

τ(q′ + (n− 1) q

) (q′ + (n− 1) q

). (2.51)

As in the generalized model, this closed-form expression reveals that the static deviation payoff in

the oligopoly model is comprised of two components. The first component can be re-written as

p(q′, q, τ(q′ + (n− 1)q))q′, and represents the static payoff that the producer obtains by deviating to q′

from q when the deviation is punished by a tax τ(q′ + (n− 1)q). The second component, τ(q′ + (n−

1)q)(q′ + (n− 1)q)/n, is the payoff accruing to the deviator when the Principal does not implement

the prescribed group punishment and instead levies no taxes.

Finally, let g (q, τ (·)) denote the maximum deviation payoff one producer can achieve from a de-

viation to q′ when other producers generate q. As in Lemma 4, we now show that as long as the

prescribed output is larger than the static Nash equilibrium output, the maximum deviation payoff

g(q, τ (·)) is minimized when the Principal levies no taxes (i.e., when τ = 0).

Lemma 10. g (q, τ (·)) ≥ g (q, τ = 0) when q ≥ qN .


Using Lemma 10, the results from Propositions 5 to 8 naturally extend to the repeated oligopoly

model, and are therefore omitted for the sake of brevity. In particular, we find that the worst

perfect-public equilibrium payoff can be attained by strategies that do not feature on-path group

punishments, and the best and the worst can be jointly characterized as solutions to (2.48)-(2.51).

Moreover, group punishments are sustainable and strictly improve welfare relative to a model where

group punishments are not allowed.

In Figure 2.1, we provide a numerical illustration of how group punishments can increase the welfare

of the team of oligopolists. In Figure 2.1a, we fix the number of producers n to ten and plot the value

of the best and worst perfect-public equilibria for each level of the discount factor δ. Note that in


Figure 2.1a, for any δ, values to the left of the static Nash equilibrium value (roughly 0.007) represent

worst equilibrium values while values to the right represent best equilibrium values. The dashed

line in Figure 2.1a shows these best and worst equilibrium values when group punishments are

allowed, while the solid line shows these values when these punishments are not allowed. Since the

dashed lines lie outside the solid lines, for all levels of the discount factor the model where taxes are

allowed yields weakly higher best equilibrium payoffs than the model where taxes are not allowed.

In particular, the repeated interaction between producers and the Principal leads to welfare gains

for intermediate values of the discount factor, and no (or relatively small) gains when the discount

factor is low or high.

For low values of δ, the Principal has weak incentives to levy the prescribed taxes. The continuation

value that producers have to promise to the Principal for implementing such taxes is too to satisfy

the feasibility constraint (2.50). As a result, very small or (approximately) no taxes can be sustained

leading to small or (approximately) no welfare gains. On the other hand, for high values of δ the

repeated interaction of producers is sufficient to guarantee the static most collusive level of output

even in the absence of the Principal.

For intermediate levels of δ, the presence of the Principal increases welfare considerably. To illus-

trate the gains associated with sustainable group punishments (or taxes), Figure 2.1b illustrates the

effect of the Principal’s punishments on the level of output in the best equilibrium. Specifically, the

solid line shows the percentage reduction in output in the best equilibrium which is obtained in our

model relative to a model where group punishments are not allowed. Observe that our model fe-

atures a most collusive output level as much as thirty percent lower than the model where group

punishments are not allowed. To achieve these lower levels of output, which correspond to higher

levels of welfare, the Principal reduces the value of the most profitable, static deviation by any of the

producers by as much as 80%. This finding suggests that the role of the Principal in the oligopoly

model is to decrease the common price to a level closer to the producer’s marginal cost in case of a

deviation, therefore reducing the value of deviations.


Figure 2.1

Equilibrium Value Sets and Group Punishments

Numerical illustration of the equilibrium value sets (panel (a)) and impact of group punishments on bestequilibrium output and best deviation payoff from best equilibrium (panel (b)).

0 0.005 0.01 0.015 0.02

Producer Payoff

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pro

duce

r D

isco

unt F

acto

r

Group Punishments Not AllowedGroup Punishments Allowed

(a)

Equilibrium Value Sets

0 0.2 0.4 0.6 0.8 1

Producer Discount Factor

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Per

cent

age

Red

uctio

n

Most Collusive OutputMost Profitable Deviation

(b)

Impact of Group Punishments

2.3.3 Substitutability and Price Externalities

In this section, we provide an overview of our additional results on how different degrees of inte-

raction between oligpolistic producers can impact the effectiveness of group punishments. A full

discussion of these results is provided in Appendix B.1.

The main point of departure of this section is the use of a new price function, which allows for dif-

ferent degrees of substitutability between producers’ output. Specifically, we make the assumption

that the inverse demand function for each producer i’s output satisfies

pi (q, τ) = αqρ−1

i

∑ni=1 qρ

i− τ, (2.52)

where α ∈ (0, 1) and ρ ∈ (0, 1) are exogenous parameters, qi is the quantity produced by producer

i and τ is the tax chosen by the Principal. This price function arises naturally in an economy where

consumers have Cobb-Douglas preferences over a bundle of individual producers’ output and a


numeraire good. In particular, the parameter α is a Cobb-Douglas parameter that governs the sub-

stitutability between the numeraire good and the bundle of producers’ output, while the parameter

ρ governs the degree of substitutability between each producer’s output. Under this formulation, a

higher level of ρ implies a higher degree of substitutability.

In the Appendix, we extend the analysis of the previous sections to the new inverse demand function

(2.52), and we analyze the relationship between the usefulness of group punishments and the sub-

stitutability parameter ρ. Specifically, we ask how the effectiveness of taxes in improving welfare

(relative to a model where taxes are not allowed) changes as the substitutability of producers’ output

changes. Our main result for this section shows that the effectiveness of taxes in improving welfare

increases as the substitutability parameter ρ increases:

Proposition 11. Fix ρ ∈ (0, 1). For n sufficiently large, there exist a δ ∈ (0, 1) and ρ > 0 such that for all

ρ′ ∈ (ρ, ρ), the welfare gains from allowing the Principal to implement group punishments are increasing in

ρ′.

Proof. See Appendix B.1.

The intuition behind the result of Proposition 11 is that when goods become more substitutable, in-

dividual producers have higher incentives to deviate from their prescribed quantities because devia-

tions have a lower negative impact on the common price. This increases the producers’ incentives to

over-produce and leads to lower equilibrium values, but also increases the relative gains from group

punishments relative to the model where these punishments are now allowed. In other words, when

goods are more substitutable and deviations are more profitable, group punishments that deter these

deviations increase welfare by more.

Finally, in Figure 2.2 we provide a numerical illustration of our result. The figure shows the value

of the best equilibrium under a low value of the substitutability parameter (ρ = 0.31) and under a

high value of the substitutability parameter (ρ = 0.83). As in Figure 2.1a, the solid lines in Figure 2.2

represent the best equilibrium payoffs in the economies where group punishments are not allowed,


and the dashed lines represent the equilibrium payoffs in the economies where group punishments

are allowed. The difference between the dashed lines and the solid lines represent the welfare gains

from allowing group punishments.

Figure 2.2

Input Substitutability and the Welfare Impact of Group Punishments

Best equilibrium values for ρ = 0.31 and ρ = 0.83 when group punishments are not allowed (solid lines) andare allowed (dashed lines). In this example, we set n = 5, α = 0.7 and c = 0.1.

Best Payoff

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13

Dis

cou

nt

Fac

tor

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ρ = 0.31ρ = 0.83

The figure provides a clear illustration of our result that group punishments yields significantly

larger increases in best equilibrium values when producers’ output is more substitutable relative

to when producers’ output is less substitutable. For example, for a discount factor of roughly 0.4,

with high degree of substitutability, the best equilibrium value when group punishments are not

allowed is roughly 0.1 while it is roughly 0.13 when they are allowed, implying a 30% gain from

group punishments. Instead, with a low degree of substitutability, the best equilibrium value when

group punishment are not allowed is roughly 0.125 while it is roughly 0.13 when they are allowed,

implying only a 4% gain from group punishments.

2.4. CONCLUSION 65

2.4 Conclusion

The potential for moral hazard is ubiquitous in team production settings and especially where the

actions of individual team members are not perfectly observable. A widely accepted principle is

that in these team production settings it is against the team’s own interest to implement a group pu-

nishment when an individual deviation has occurred. An outsider is therefore needed to implement

the team’s first-best level of production.

In a generalized repeated team production model, we show that the team can always sustain self-

imposed group punishments after aggregate outcomes are observed when team members’ utility

interacts in non-trivial ways with aggregate team outcomes. Moreover, we provide conditions un-

der which the threat of these punishments improves the welfare of the team relative to a model

where group punishments are not part of the team’s action set. Using the repeated oligopoly mo-

del of Abreu (1986) as an application, we show that team self-imposed group punishments are most

effective in improving team welfare when team members are sufficiently patient and when their

contributions to the aggregate outcome are more substitutable.

Our theoretical results provide direct guidance for future applied and empirical research. In par-

ticular, our model predicts that team production environments featuring a strong interaction bet-

ween aggregate outcomes and individual utilities are also environments where self-inflicted group

punishments can provide large welfare gains to the team. Economic unions such as the European

Union are particularly good examples of teams where team members have historically been tempted

to deviate from their prescribed actions, and where aggregate team outcomes (e.g. common interest

rates and exchange rates) interact in non-trivial ways with the individual utility of team members

(e.g. individual output). Large corporations with multiple project managers are another setting to

apply our model, especially since the presence of a non-benevolent top management lacking commit-

ment to group punishments might exacerbate the moral hazard problem among individual project

managers. Additional settings relevant to our analysis include environmental pacts, workplace ma-

nagement, and cartels. The analysis of the interaction between team members and the quantification


of possible welfare gains from implementing group punishments in these settings constitutes in our

opinion areas of fruitful future research.

Chapter 3

Advertising, Consumption, and AssetPrices

67

68 CHAPTER 3. ADVERTISING, CONSUMPTION, AND ASSET PRICES

3.1 Introduction

The post-war period has seen a steady increase in aggregate advertising, and a dramatic evolution

in the way companies use advertising to induce the purchase of their products. The introduction

of new means of communication such as television and the internet has been quickly followed by

the effort of companies to use these new means to inform potential customers about their products.

Despite the existence of an entire field of economics studying how advertising can influence con-

sumption choices (Bagwell (2007)), and despite the central role that consumption plays in modern

financial economics, surprisingly little research has however analyzed the implications for finan-

cial economics of the advertising-consumption relation. This paper aims to be the first to explore

these implications, both empirically and theoretically, through the lens of consumption-based asset

pricing.

I begin by documenting an empirical relationship between aggregate advertising expenditures, con-

sumption and equity returns in the United States. I first show that aggregate advertising growth

predicts future aggregate consumption growth at annual horizons of one to two years. This predic-

tability relation is time-varying and holds across different robustness tests in post-war data. Then,

I show that advertising and consumption growth together predict excess returns, and they do so

better than most predictors such as the dividend-price ratio and the dividend payout ratio. In parti-

cular, high advertising growth predicts high future returns, and high consumption growth predicts

low future returns.

I build a model of frictional search in the goods market to replicate the predictability found in the

data. The model features two goods, one of which is exogenously endowed to households. The

second good is sold by firms on a goods market characterized by two frictions. The first friction is

an informational friction such that, absent advertising, households are only aware of the existence

of their endowment. Firms use advertising to overcome this friction and search for new customers

among the households. Once a firm attracts a household, the firm and the household form a cus-

tomer relationship that lasts for multiple (as in Gourio and Rudanko (2014)). The second friction is


an advertsing externality that makes the customer search process more difficult for each firm whe-

never advertising by other firms is high. Following the labor search literature, I call this externality

a goods market congestion effect. The model has direct implications for the impact of advertising

and customer relationships on household consumption and equity returns. On the household side,

advertising shifts consumption away from the endowment good and creates a persistent component

in the consumption of goods produced by firms. On the firm side, customers are risky assets. In bad

times, firms may want to decrease their stock of customers but they are prevented from doing so

because their advertising cannot be negative. Conversely, in good times firms would like to increase

their customers, but because advertising by other firms is also high the congestion effect makes their

advertising less effective in attracting new customers.

The model is able to replicate the predictive power of advertising growth and consumption growth

on equity returns, as advertising growth induces negative co-variation between expected marginal

utility and equity returns. High advertising growth shifts expected consumption away from the nu-

meraire and therefore increases the numeraire’s expected marginal utility. At the same time, high

advertising growth lowers expected returns from advertising, which in the model are paid in units

of the endowment good. This happens because i) high growth in advertising reduces the future mar-

ginal revenues of the firm and ii) high advertising growth at the individual firm level generates high

aggregate advertising growth which reduces the likelihood for individual firms to attract new cus-

tomers. Put together, these conditions imply that times when advertising growth is high are times

of low expected returns, high expected marginal utility and high returns. Finally, the results show

that the goods market congestion effect is a key element in driving the predictive power of adverti-

sing growth on excess returns. To compensate the externalities arising from advertising individual

firms widely vary their advertising decisions depending on the state of the economy. The model

therefore generates large shifts in advertising growth that map into large shifts in the growth of con-

sumption, marginal utility and marginal profits, and that drive the predictive power of advertising

on future consumption and returns. A counterfactual exercise shows that, absent any goods market

congestion, the predictive power of advertising growth on excess returns vanishes.


Related Literature The contribution of the paper to the literature is twofold. First, the paper provi-

des empirical evidence supporting the idea that standard consumption-based asset pricing models

hold when conditioning on variables that provide information about agents’ future expectations

(Campbell and Cochrane (2000)). Different from the previous literature, which conditions on vari-

ables that contain a price and therefore directly predict future expected returns (Ferson and Schadt

(1996), Jagannathan and Wang (1996), Cochrane (1996) and Lettau and Ludvigson (2001b)), I ho-

wever predict returns using advertising through the channel of future expected consumption. My

results are in this sense close to those in Savov (2011).1 Second, this is the first paper to explore

the theoretical implications of advertising, goods market frictions and customer capital for aggre-

gate consumption and asset pricing. In this respect, my work relates to two strands of literature.

From the macroeconomics standpoint, frictions in the goods market have been recently shown to be

a key ingredient in generating features observed in business cycles. Petrosky-Nadeau and Wasmer

(2015) demonstrate goods market frictions as an intuitive way to endogenously generate persistent

business cycle fluctuations. In a similar spirit, Den Haan (2013) analyzes the role of inventories as

coming from imperfect market clearing in generating business cycles, while Storesletten et al. (2011)

show that goods-market frictions allow a model with demand shocks to match most of the features

of a standard model with productivity shocks. Finally, Hall (2014) relates the pro-cyclical variation

of advertising expenditures to macroeconomic wedges, and in particular to frictions in the goods

market. From the financial economics standpoint, my work builds on two recent sub-fields of the

production-based asset pricing literature (Cochrane (1991, 1996) and Jermann (1998)). The first builds

on Berk et al. (1999) to analyze the impact of growth options in intangible capital (Ai et al. (2013)),

organization capital (Eisfeldt and Papanikolaou (2013)) and brand capital (Belo et al. (2014b) and

Vitorino (2014)) on the cross-section of expected stock returns. The second focuses on how search

frictions in the labor market affect asset prices (Kuehn et al. (2012), Belo et al. (2014a) and Kuehn

et al. (2017)). Finally, from a modeling point of view the two papers most closely related to mine

are Drozd and Nosal (2012) and Gourio and Rudanko (2014), which however respectively focus on

international prices and the cross section of firm characteristics.

1He uses garbage as a measure of realized consumption to test the consumption-based asset pricing model, while I useadvertising as a measure of expected consumption.

3.2. AGGREGATE ADVERTISING EXPENDITURES AND EQUITY RETURNS 71

3.2 Aggregate Advertising Expenditures and Equity Returns

Robert J. Coen from the advertising company Erickson-McCann used to regularly publish data on

aggregate advertisement expenditures in the United States. The dataset ranges from 1900 to 2007

and includes, among other variables, U.S. aggregate expenditures for advertising on newspapers,

periodicals, yellow pages, radio, television and internet.2 In Figure 3.1, I explore the time-series

evolution and composition of post-war advertising by breaking the variable in two broad categories,

physical and non-physical advertising. I define physical advertising as the sum of advertising on

newspapers, periodicals, magazines, direct mail, yellow pages, farm publications, billboards and

business papers, and non-physical advertising as the sum of advertising on radio, television, and

internet. The Figure shows that the level of aggregate advertising expenditures in the US is five

times larger in the late 2000s than in the 1950s, and that advertising growth is mainly due to physical

advertising growth. Second, traditional physical advertising and modern non-physical advertising

are complements rather than substitutes. Despite the advent of television and internet advertising

and the increasing relative importance of these channels (Panel B), the average U.S. company in 2010

still spends more than twice as much in physical than in non-physical advertising.

In Figure 3.2, Panel A, I compare the post-war evolution of per-capita advertising expenditures and

per-capita consumption in the United States. The data for consumption come from personal con-

sumption expenditures in the NIPA tables, and both advertising expenditures and consumption are

expressed in 2005 US dollars, using the Consumer Price Index (CPI) for consumption and the Produ-

cer Price Index (PPI) for advertising expenditures.3 As extensively documented in the literature (see

Hall (2014) and references therein), advertising is a pro-cyclical variable, and therefore highly corre-

lated (but not cointegrated, see Appendix C.1) with consumption. In Panel B I plot the advertising-

consumption ratio. The Figure shows that the ratio is a slowly-moving process, decreasing during

recessions in the late 80s and early 2000s and expansions in the 50s and 90s expansions.

2The data can be found on Douglas Galbi’s website: http://purplemotes.net/2008/09/14/us-advertising-expenditure-data/. For the years 2007 to 2010, Hall (2014) updates this dataset using revenue data from companies in the informationsector published by the Census Bureau. These data are no longer available, but can be found on Hall’s website.

3I keep this definition of consumption through the rest of the paper. The main results of the paper hold when I usemore granular definitions of consumption such as consumption of nondurable goods, durable goods and services.

http://purplemotes.net/2008/09/14/us-advertising-expenditure-data/

http://purplemotes.net/2008/09/14/us-advertising-expenditure-data/


Figure 3.1

Expenditures in Physical and Non-Physical Advertising in the U.S., 1950-2010

Physical advertising is the sum of advertising on newspapers, periodicals, magazines, direct mail, yellowpages, farm publications, billboards and business papers. Non-physical advertising includes radio, televisionand internet. Total advertising is the sum of physical and non-physical advertising. The advertising data forthe years 1900-2007 are hand-collected by Robert J. Coen from the advertising company Erickson-McCann andcan be found on Douglas Galbi’s website. For the years 2007 to 2010, Hall (2014) updates this dataset usingrevenue data from companies in the information sector published by the Census Bureau. These data are nolonger available, but can be found on Hall’s website. All the data are expressed in 2005 US billion dollars usingthe producer price index.

010

020

030

0

1940 1960 1980 2000 2020Year

TotalPhysicalNon−Physical

Panel A: Total Advertising, USD Billions

.15

.2.2

5.3

.35

1940 1960 1980 2000 2020Year

Panel B: Share of Non−Physical Advertising

In Figure 3.3, I finally plot advertising growth, consumption growth and excess returns on U.S. equity

in the post-war period. The data for excess returns, defined as the yearly returns on the S&P 500

minus the one-year interest rate, come from Robert Shiller’s website. Panel A of the Figure shows

that the growth rates in advertising and consumption are highly correlated, advertising growth is

more volatile than consumption growth and (especially after 1980) leads consumption growth. Panel

B similarly shows a positive correlation between advertising growth and excess returns on equity.

3.2.1 Consumption Growth and Excess Returns Predictability

In this Subsection I show that advertising expenditures growth predicts consumption growth at pre-

dictive horizons of one to two years, and that advertising and consumption growth jointly predict

excess returns at horizons of one to four years. Table 3.1 shows summary statistics for advertising

expenditures growth, consumption growth and other known predictors.


Figure 3.2

Per-Capita Consumption and Advertising in the U.S., 1950-2010

Consumption is Personal Consumption Expenditures from NIPA Tables, expressed in 2005 US dollars usingthe Consumer Price Index. Advertising is the sum of advertising on newspapers, periodicals, magazines,direct mail, yellow pages, farm publications, billboards, business papers, radio, television and internet. Theadvertising data for the years 1900-2007 are hand-collected by Robert J. Coen from the advertising companyErickson-McCann and can be found on Douglas Galbi’s website. For the years 2007 to 2010, Hall (2014) updatesthis dataset using revenue data from companies in the information sector published by the Census Bureau.These data are no longer available, but can be found on Hall’s website. Advertising expenditures is expressedin 2005 US dollars using the producer price index.

200

400

600

800

1000

1000

015

000

2000

025

000

3000

0

1940 1960 1980 2000 2020Year

Consumption (left axis)

Advertising (right axis)

Panel A: Per−Capita Consumption and Advertising

.02

.025

.03

.035

.04

1940 1960 1980 2000 2020Year

Panel B: Advertising−Consumption Ratio


Figure 3.3

Advertising Expenditures Growth, Consumption Growth and Excess Returns in the U.S.,1950-2010

Consumption is Personal Consumption Expenditures from NIPA Tables. The advertising data for the years1900-2007 are hand-collected by Robert J. Coen from the advertising company Erickson-McCann and can befound on Douglas Galbi’s website. For the years 2007 to 2010, Hall (2014) updates this dataset using revenuedata from companies in the information sector published by the Census Bureau. These data are no longer avai-lable, but can be found on Hall’s website. Advertising is the sum of advertising on newspapers, periodicals,magazines, direct mail, yellow pages, farm publications, billboards, business papers, radio, television and in-ternet. Excess returns are yearly returns on the S&P 500 minus the one-year interest rate from Robert Shiller’swebsite.

−.2

−.1

0.1

.2

1940 1960 1980 2000 2020Year

Consumption Growth Advertising Growth

Panel A: Real Advertising and Consumption Growth

−.4

−.2

0.2

.4

1940 1960 1980 2000 2020Year

Excess Returns Advertising Growth

Panel B: Advertising Growth and Excess Returns


Advertising growth (∆a) has a mean of 2.3 percent and a standard deviation of 5.6 percent, respecti-

vely three times higher than consumption growth. The variable is positively correlated with the

dividend-price ratio, the earnings-price ratio and the payout ratio, so that times when corporate ear-

nings are high are also times when advertising expenditures are high. Moreover, ∆a is positively

correlated with the Lettau and Ludvigson (2001a) cointegrating residual cay, so that advertising ex-

penditures grow whenever whenever consumption is above its long-run equilibrium level. Finally,

consumption and advertising growth are mildly autocorrelated with AR(1) coefficients of 0.27 and

0.39 (t-statistics of 2.04 and 3.04), respectively, but the null hypothesis of a unit root in augmented

Dickey and Fuller (1979) tests is rejected for these two time series (the p-values of the tests are equal

to zero up to four decimal points).

Table 3.2 presents the main empirical results of the paper, the predictive power of advertising gro-

wth on consumption growth and the predictive power of advertising and consumption growth on

excess returns on equity. Panel A reports coefficient estimates and associated Hansen and Hodrick

(1980) t−statistics for predictive regressions of cumulative consumption growth from year t to year

t + τ (∆ct→t+τ), using lagged consumption growth and lagged advertising growth as predictors. In the

Table, the predictive horizon τ varies from one to four years. Specification (2) shows that lagged con-

sumption growth predicts future consumption growth only up to one year in the future. Specifica-

tions (1) and (3) show that advertising expenditures predict consumption growth at horizons of one

and two years. In particular, specification (3) shows that the predictive power of current consump-

tion growth in forecasting future consumption growth in specification (2) arises from the component

of consumption growth correlated to advertising growth.4 Section 3.2.2 and Appendix C.1 provide

additional robustness tests for the predictive power of consumption growth on advertising growth.

Panel B of Table 3.2 similarly reports the coefficient estimates and t-statistics for predictive regressi-

ons of cumulative excess returns (rxt→t+τ), using the same predictors as in Panel A. Specifications (1)

to (3) show that even if consumption growth and advertising growth do not predict excess returns

individually (but consumption at long horizons), together they predict excess returns at any horizon

4As an additional experiment, I regress consumption growth on a constant and advertising growth, and use the re-sulting residual to predict cumulative consumption growth. The null hypothesis of no predictive power of the residualcannot be rejected for any horizon from one to four years (p-values of 0.996, 0.448, 0.423 and 0.457, respectively).


Table 3.1

Summary Statistics for Predictors, Post-War Period

The Table gives summary statistics for advertising expenditures growth (∆at), consumption growth (∆ct), aswell as other known stock returns predictors. Consumption is Personal Consumption Expenditures from NIPATables. Advertising is the sum of advertising on newspapers, periodicals, magazines, direct mail, yellow pages,farm publications, billboards, business papers, radio, television and internet. The advertising data for the years1900-2007 are hand-collected by Robert J. Coen from the advertising company Erickson-McCann and can befound on Douglas Galbi’s website. For the years 2007 to 2010, Hall (2014) updates this dataset using revenuedata from companies in the information sector published by the Census Bureau. These data are no longeravailable, but can be found on Hall’s website. log dpt and log pet are respectively the log price-dividend ratioand the cyclically-adjusted log price-earnings ratio, both from Robert Shiller’s website. payt is the net payoutyield from Michael Roberts’s website. The default spread de ft is the difference between the yield of Baa andAaa corporate bonds, while the term spread termt is the difference between the yield of a 10 year constantmaturity U.S. government bond and the yield on a 3 month constant maturity U.S. T-bill. The inflation rateπt is the growth rate of the Consumer Price Index. The data for de ft , termt and πt comes from FRED. Thedata for the consumption-wealth cointegrating residual cayt comes from Martin Lettau’s website. ADF is theaugmented Dickey and Fuller (1979) test statistic.

Mean St. Dev. Max. Min. Corr. ∆at AR(1) t-stat ADF p-value Range

∆at 0.023 0.056 0.136 -0.132 1.000 0.387 3.035 -4.361 0.000 1950-2010∆ct 0.022 0.018 0.054 -0.019 -0.060 0.269 2.044 -4.446 0.000 1950-2010

log dpt -3.501 0.423 -2.669 -4.448 0.122 0.932 19.016 -1.843 0.359 1950-2012log pet 2.755 0.410 3.833 1.985 -0.079 0.843 11.858 -2.651 0.083 1950-2012

payt 0.115 0.021 0.161 0.054 0.149 0.787 12.451 -3.026 0.033 1950-2010de ft 0.943 0.420 2.320 0.000 -0.105 0.838 18.452 -3.586 0.006 1950-2014

termt 1.810 1.072 3.490 -0.060 0.122 0.480 2.496 -4.034 0.001 1950-2014πt 0.037 0.029 0.139 -0.007 -0.315 0.739 8.655 -3.079 0.028 1950-2013

cayt -0.000 0.017 0.033 -0.036 0.272 0.887 14.948 -1.360 0.601 1952-2013


Table 3.2

Consumption Growth and Excess Returns Predictability, Post-War Period

The Table shows coefficient estimates for cumulative consumption growth (∆ct→t+τ) and excess returns (rxt→t+τ)

predictive regressions using lagged advertising expenditures growth (∆at−1→t) and consumption growth(∆ct−1→t) as predictors. Excess returns are yearly returns on the S&P 500 minus the one-year interest ratefrom Robert Shiller’s website. The t-statistics in parentheses are computed using Hansen and Hodrick (1980)standard errors. R2

adj and F are the adjusted R-squared and F-statistics, respectively.

Panel A: Consumption Growth Panel B: Excess Returns∆ct→t+1 ∆ct→t+2 ∆ct→t+3 ∆ct→t+4 rx

t→t+1 rxt→t+2 rx

t→t+3 rxt→t+4

(1) ∆at−1→t 0.129 0.160 0.128 0.085 0.293 0.476 0.956 0.910(3.25) (2.10) (1.20) (0.67) (0.78) (0.76) (1.12) (0.83)

R2adj 0.143 0.074 0.018 -0.007 -0.007 -0.005 0.015 0.001

(2) ∆ct−1→t 0.266 0.183 0.043 -0.069 -2.127 -3.291 -4.020 -6.191(2.03) (0.75) (0.14) (-0.19) (-1.92) (-1.84) (-1.74) (-2.13)

R2adj 0.051 -0.006 -0.018 -0.018 0.040 0.046 0.045 0.067

(3) ∆at−1→t 0.127 0.201 0.195 0.161 1.203 1.900 2.936 3.626(2.47) (2.00) (1.33) (0.91) (2.92) (2.88) (3.18) (2.93)

∆ct−1→t 0.010 -0.214 -0.337 -0.380 -4.404 -6.887 -9.579 -13.477(0.07) (-0.71) (-0.79) (-0.74) (-3.42) (-3.46) (-3.62) (-3.72)

R2adj 0.128 0.067 0.016 -0.010 0.128 0.148 0.215 0.224F 5.049 2.186 0.859 0.397 6.037 6.219 6.829 6.718

from one to four years. In particular, conditional on consumption growth high current advertising

growth predicts high future excess returns.

In Table 3.3, I compare the predictive power of advertising and consumption growth to the pre-

dictive power of the predictors summarized in Table 3.1. As the previous literature documents, the

dividend-price price-earnings ratios are effective at predicting long-horizon returns, while the pre-

dictive power of the payout ratio and term spread decreases with the predictive horizon. Advertising

and consumption growth, similar to cay, have high predictive power at any predictive horizon. The

term spread is the only variable that has stronger predictive power (as measured by the predictive

regression’s R-squared) than advertising and consumption at any horizon, while cay has higher pre-

dictive power at horizons of three and four years.


Table 3.3

Excess Returns Predictive Regressions, Post-War Period

The Table shows coefficient estimates for cumulative excess returns (rxt→t+τ) predictive regressions using lagged

growth in advertising (∆at−1→t, conditional on lagged consumption growth ∆ct−1→t) as well as other variables,as predictors. Excess returns are yearly returns on the S&P 500 minus the one-year interest rate from RobertShiller’s website. The reported t-statistics are computed using Hansen and Hodrick (1980) standard errors.R2

adj is the adjusted R-squared statistics.

rxt→t+1 rx

t→t+2 rxt→t+3 rx

t→t+4Coeff. t-stat R2

adj Coeff. t-stat R2adj Coeff. t-stat R2

adj Coeff. t-stat R2adj

∆at−1→t 1.20 2.92 0.13 1.90 2.88 0.15 2.94 3.18 0.21 3.63 2.93 0.22∆ct−1→t -4.40 -3.42 -6.89 -3.46 -9.58 -3.62 -13.48 -3.72

log dpt−1 0.10 2.01 0.05 0.18 2.04 0.09 0.25 1.71 0.11 0.38 1.81 0.16log pet−1 -0.04 -0.86 -0.01 -0.07 -0.82 -0.00 -0.11 -0.82 0.01 -0.23 -1.15 0.04

payt−1 2.51 2.74 0.09 3.85 2.27 0.10 4.96 1.80 0.10 6.64 1.76 0.12de ft−1 0.01 0.14 -0.02 -0.04 -0.45 -0.01 -0.04 -0.31 -0.01 -0.02 -0.11 -0.02

termt−1 0.07 2.65 0.16 0.11 2.36 0.19 0.14 2.10 0.19 0.19 2.08 0.20πt−1 -0.44 -0.65 -0.01 -1.12 -0.91 0.00 -1.31 -0.69 -0.00 -0.50 -0.19 -0.02

cayt−1 2.55 2.30 0.05 5.11 2.65 0.11 8.11 2.96 0.19 11.33 3.23 0.25

In Table 3.4, I run tri-variate excess returns predictive regressions using advertising growth, con-

sumption growth and one of the other predictors as regressors, in the spirit of Huang (2015). For

every predictive horizon I consider, advertising growth (and consumption growth, omitted in the

Table) is always a significant predictor of excess stock returns. The only variables that are jointly sta-

tistically significant with advertising and consumption growth are the term spread and the payout

ratio. For horizons of two years, the default spread, inflation and cay are jointly significant. Finally,

at horizons of three and four years, cay is the only jointly significant predictor of excess returns.

3.2.2 Robustness

Table 3.5 shows the results of the estimation of a Vector-Autoregressive model of order two for ad-

vertising and consumption growth. The estimation results show that advertising growth is predicted

by consumption growth and is autocorrelated conditional on advertising growth. On the other hand,


Table 3.4

Tri-Variate Excess Returns Predictive Regressions, Post-War Period

The Table shows coefficient estimates for cumulative excess returns (rxt→t+τ) predictive regressions using the

lagged growth in advertising (∆at−1→t) and consumption (∆ct−1→t, omitted in the Table) in tri-variate regres-sions with other predictors. Excess returns are yearly returns on the S&P 500 minus the one-year interestrate from Robert Shiller’s website. The reported t-statistics are computed using Hansen and Hodrick (1980)standard errors. R2


rxt→t+1 rx

t→t+2Coeff. t-stat

Coeff. t-stat R2adj F Coeff. t-stat

Coeff. t-stat R2adj F

∆at−1 ∆at−1 ∆at−1 ∆at−1

log dpt−1 1.05 2.40 0.07 1.54 0.14 4.89 1.57 2.26 0.14 1.85 0.19 4.79log pet−1 1.20 2.78 -0.00 -0.08 0.11 4.01 1.87 2.74 -0.02 -0.24 0.13 4.12

log payt−1 1.01 2.39 1.68 2.02 0.16 5.65 1.60 2.38 2.59 1.79 0.18 5.06de ft−1 1.28 3.16 -0.05 -1.23 0.13 4.54 2.11 3.47 -0.14 -2.15 0.18 6.69

termt−1 1.48 2.47 0.05 1.94 0.27 4.57 1.49 1.53 0.08 1.88 0.22 2.76πt−1 1.21 3.07 -0.93 -1.68 0.16 5.67 1.87 3.06 -2.00 -2.13 0.21 6.88

cayt−1 1.01 2.26 1.83 1.74 0.16 6.11 1.45 2.15 4.06 2.36 0.23 7.29

rxt→t+3 rx

t→t+4Coeff. t-stat

Coeff. t-stat R2adj F

Coeff. t-statCoeff. t-stat R2

adj F∆at−1 ∆at−1 ∆at−1 ∆at−1

log dpt−1 2.54 2.74 0.17 1.47 0.25 4.71 2.91 2.32 0.26 1.57 0.29 4.60log pet−1 2.88 3.13 -0.03 -0.29 0.20 4.48 3.43 2.81 -0.08 -0.52 0.22 4.41

log payt−1 2.61 2.83 2.87 1.31 0.24 4.85 3.10 2.52 4.34 1.44 0.26 4.85de ft−1 3.20 3.68 -0.17 -1.78 0.25 6.37 3.82 3.24 -0.17 -1.16 0.24 5.36

termt−1 2.18 1.63 0.10 1.57 0.25 2.50 2.83 1.81 0.15 1.70 0.32 3.43πt−1 2.89 3.34 -2.26 -1.65 0.26 6.47 3.85 3.63 -2.82 -1.61 0.33 8.33

cayt−1 2.17 2.50 5.92 2.63 0.31 7.71 2.58 2.60 7.91 2.97 0.38 10.04


Table 3.5

VAR Model for Advertising and Consumption Growth, Post-War Period

The Table shows coefficient estimates for a Vector-Autoregressive (VAR) model of advertising expenses andconsumption growth (∆a and ∆c, respectively). The t-statistics are in parentheses. In each equation, R2 and Fare the R-squared and F-statistics, respectively.

Panel A: One Lag Panel B: Two Lags∆at→t+1 ∆ct→t+1 ∆at→t+1 ∆ct→t+1

∆at−1→t 0.679 0.127 0.515 0.124(4.71) (2.52) (3.23) (2.16)

∆at−2→t−1 0.242 -0.0167(1.49) (-0.28)

∆ct−1→t -1.417 0.0105 -1.119 0.0681(-3.11) (0.07) (-2.39) (0.41)

∆ct−2→t−1 -1.180 0.00771(-2.38) (0.04)

R2 0.274 0.158 0.336 0.170F 11.12 5.521 7.333 2.973

consumption growth is not conditionally autocorrelated and is predicted by advertising expenditu-

res growth.

Table 3.6 shows the results of Table 3.5 for different sub-samples of my dataset. In Panel A, I re-

port the results for the 1922-2009 sample, while in Panel B for the 1982-2009 sample.5 The results

show that the dynamics of the advertising-consumption relationship dynamic dramatically change

over the course of the last century. The sign of the VAR coefficients does not change across diffe-

rent samples, but their magnitude and statistical significance increases when I restrict the sample to

more recent years. The time-varying relation between advertising growth and consumption growth

therefore limits the use of advertising growth as an instrumental variable for expected consumption

growth, and rathers calls for a model to explore the joint dynamics of the variables.

5Tests for cointegration between consumption and advertising in these two samples fail to reject the null hypothesis ofno cointegration.


Table 3.6

VAR Model for Advertising and Consumption Growth, 1922-2009 and 1982-2009

The Table shows coefficient estimates for a Vector-Autoregressive (VAR) model of advertising expenses andconsumption growth (∆a and ∆c, respectively) across different samples. The t-statistics are in parentheses. Ineach equation, R2 and F are the R-squared and F-statistics, respectively.

Panel A: 1922-2009 Panel B: 1982-2009One Lag Two Lags One Lag Two Lags

∆at→t+1 ∆ct→t+1 ∆at→t+1 ∆ct→t+1 ∆at→t+1 ∆ct→t+1 ∆at→t+1 ∆ct→t+1

∆at−1→t 0.352 0.0666 0.301 0.0433 0.783 0.166 0.454 0.117(2.97) (1.16) (2.39) (0.70) (4.10) (3.37) (2.73) (2.25)

∆at−2→t−1 0.0602 0.0572 0.856 0.137(0.49) (0.95) (4.53) (2.31)

∆ct−1→t -0.242 0.140 -0.190 0.159 -1.312 0.224 -1.614 0.155(-0.95) (1.13) (-0.73) (1.25) (-1.95) (1.29) (-2.36) (0.72)

∆ct−2→t−1 -0.124 -0.0885 -1.900 -0.261(-0.47) (-0.70) (-3.15) (-1.38)

R2 0.0966 0.0612 0.0825 0.0676 0.383 0.543 0.651 0.604F 4.759 2.900 1.978 1.596 8.992 17.24 13.06 10.70


Table 3.7

Consumption Growth Predictive Regressions, Post-War Period

The Table shows coefficient estimates for cumulative consumption growth (∆ct→t+τ) predictive regressionsusing lagged consumption growth (∆ct−1→t), advertising expenditures growth (∆at−1→t), as well as the laggedshort-term interest rate (r3m

t−1) and lagged term spread from t− 1 to t− 1 + τ (rτt−1 ) (Harvey (1988)) as predictors.

The short-term interest rate is the yield on a 3 month constant maturity U.S. T-bill, and the term spread is thedifference between a U.S. government bond with constant maturity τ and the short-term interest rate. The datais from FRED. The t-statistics in parentheses are computed using Hansen and Hodrick (1980) standard errors.R2


∆ct→t+1 ∆ct→t+2 ∆ct→t+3 ∆ct→t+4

(1) r3mt−1 0.001 0.001 0.003 0.071

(0.85) (0.26) (0.81) (0.70)rτ

t−1 0.020 0.030 0.023 0.063(1.82) (2.81) (1.80) (0.65)

R2adj 0.172 0.272 0.146 0.072F 2.590 3.669 1.588 0.654

(2) ∆at−1→t 0.149 0.395 0.541 0.629(2.36) (3.51) (3.07) (3.25)

∆ct−1→t 0.241 -0.281 -0.786 -1.104(1.21) (-0.76) (-1.38) (-1.65)

r3mt−1 -0.000 -0.002 -0.001 0.023

(-0.38) (-1.17) (-0.43) (0.29)rτ

t−1 0.010 0.013 0.009 0.022(1.14) (1.59) (0.87) (0.29)

R2adj 0.475 0.519 0.351 0.305F 7.511 6.196 3.154 2.599

In Table 3.7, I test the robustness of advertising growth in predicting consumption growth, by aug-

menting specification (3) of Table 3.2 with an additional predictor. To the best of my knowledge, the

term structure of the interest rates is one of the few variables known to predict consumption growth

at long horizons. I follow Harvey (1988) and run consumption growth predictive regressions using

the short-term risk-free rate and the term spread as a proxy for the term structure. Specification (1)

of Table 3.7 confirms that the term structure is a good predictor of consumption growth at horizons

from one to three years. Specification (2) shows that the predictive power of advertising growth

significantly decreases the predictive power of the term structure at any predictive horizon.

3.3. MODEL 83

Figures 3.4 and Table 3.8 report the results of my third robustness test, which measures the out-of-

sample performance of advertising growth in predicting excess returns using both moving-window

and expanding-window regressions. In moving-window regressions, I use a fixed rolling window of

fifty observations as fitting sample. In expanding-window regressions, I start with fitting the model

on the first fifty annual observations, and expand the sample one observation at a time to obtain the

full 1950-2010 sample. Figure 3.4 plots point estimates for the coefficients of one-year-ahead excess

returns predictive regressions, as well as their associated 95 percent confidence intervals, for the out-

of-sample period 1980-2010. In both moving regressions (Panel A) and expanding regressions (Panel

B), the regression coefficient associated to advertising growth is around one (but for years 2003-2008

in moving regressions), and always statistically different from zero at a 95 percent confidence level.

Finally, Table 3.8 reports the results of the out-of-sample R-squared statistics of Campbell and Thomp-

son (2008) and the adjusted mean squared prediction error (MSPE) statistics of Clark and West (2007).

The out-of-sample R-squared displays similar values in moving and expanding regressions. The

within-sample R-squared increases with the predictive horizon. The adjusted-MSPE statistics speaks

in favor of long-run predictability. The (one-sided) t-statistic for a difference in predictive accuracy

between within sample and out-of-sample predictions is rejected in both moving and expanding

regressions at a five percent confidence level for horizons of two to four years.

Finally, in Appendix C.2 I show that advertising growth predicts a component of aggregate con-

sumption growth not captured by the Bansal and Yaron (2004) long-run risk. In the next Section, I

introduce a dynamic investment-based asset pricing model of frictions in the goods market to repli-

cate the observed predictive power of advertising expenditures on aggregate consumption growth

and excess returns.

3.3 Model

The model is a discrete-time, dynamic stochastic general equilibrium model with two goods. The

economy is populated by a continuum of identical households and a continuum of identical firms.


Figure 3.4

Coefficient Estimates in Out-of-Sample Excess Returns Predictive Regressions, 1980-2010

Growth in advertising expenditures and consumption are used to predict excess returns in the next year, whereexcess returns are the yearly returns on the S&P 500 minus the one-year interest rate from Robert Shiller’swebsite. Panel A reports point estimates and 95% confidence intervals for the slope coefficient of advertisingexpenditures, using a regression with a rolling window of 50 periods (years). Panel B reports point estimatesand 95% confidence intervals for the slope coefficient of relative advertising expenditures, using an expandingregression with an initial length of 50 periods (years).

1980 1985 1990 1995 2000 2005 20100

1

2

3Panel A: Moving Regressions

Year1980 1985 1990 1995 2000 2005 20100

1

2

3Panel B: Expanding Regressions

3.3. MODEL 85

Table 3.8

Out-of-Sample Excess Returns Predictive Regressions

The Table shows the out-of-sample performance of cumulative excess returns (rxt→t+τ) predictive regressions

using lagged growth in advertising (∆at−1→t) and consumption (∆ct−1→t) as predictors. The statistic R2ws is the

within-sample adjusted R-squared statistic. Out-of-sample moving regressions use a 30-year rolling windowto predict cumulative excess returns at different horizons, starting from 1980. Out-of-sample expanding regres-sions use the initial 1950-1980 sample to predict cumulative excess returns at different horizons. The procedureis then repeated by expanding the sample in one-year steps until the full 1950-2010 sample is obtained. Thestatistic R2

osis the out-of-sample R-squaredd statistic detailed in Campbell and Thompson (2008). The Newey-West (NW) t-statistics are obtained from regressing the adjusted-MSPE statistics of Clark and West (2007) on aconstant. The test is a one-side test for a zero coefficient.

Within-Sample Out-of-Sample Moving Out-of-Sample ExpandingHorizon (years) R2

ws R2os NW t-stat. R2

os NW t-stat.

1 0.128 0.071 1.216 0.066 1.3852 0.148 0.129 1.916 0.114 2.0173 0.215 0.153 2.005 0.147 2.4194 0.224 0.139 2.349 0.177 3.178

The model features two key frictions. First, absent advertising households in the economy are only

aware of the existence of their endowment (numeraire) good. Firms overcome this friction by spen-

ding resources to advertise their product. Once firms and customers match with each other, they

form a relationship that lasts for multiple periods. Second, the advertising process is subject to se-

arch externalities. Times when all the firms in the economy post many advertisements are also times

when it is harder for an individual firm to attract a customer by posting an advertisement (ad). In

particular, once every firm has posted its ad’s, the sum of the individual ad’s in the economy de-

termines the probability that one ad will turn into a customer for an individual firm.6 I denote this

probability by λ. I assume that product search is costless for the household, and normalize the hou-

sehold search cost to one. Using a den Haan et al. (2000) function with elasticity ϑ > 0, the matching

function between a household and an ad is given by

G (ad) =ad(

1 + adϑ)1/ϑ

. (3.1)

6For tractability, I abstract from the difference between customer and marketing/brand capital (Drozd and Nosal(2012)), where advertising expenditures build marketing capital, which in turn determines the likelihood of attractingnew customers.


Denoting aggregate variables with uppercase letters, the probability λ that an advertisement attracts

a household is a function of the total ad’s in the economy:

λ (AD) =G (AD)

AD=

1(1 + ADϑ

)1/ϑ. (3.2)

Finally, customer relations are long-lasting. I denote the stock of firm customers (customer capital,

Gourio and Rudanko (2014)) by n and assume that in each period t the firm loses an exogenous

fraction ϕ ∈ [0, 1] of its customers. The aggregate law of motion for customer capital between period

t and period t + 1 is then

Nt+1 = (1− ϕ) Nt + G (ADt) (3.3)

= (1− ϕ) Nt + λ (ADt) ADt. (3.4)

3.3.1 Firm Problem and Return on Equity

Firms enter each time period with a stock of customers, observe the aggregate endowment of the

numeraire good and decide how much to spend in advertising to build their customer capital. Firm

revenue is the product between the unit price of the manufactured good and the number of firm

customers. Moreover, firms pay a convex advertising cost to attract customers. Three assumptions

on firm profits allow to simplify the analysis while retaining the model’s main insights. First, firms

extract all the matching surplus from households, so that the manufactured good’s price is the mar-

ginal rate of intratemporal substitution between the manufactured good and the numeraire. This

eliminates the issue of time-inconsistent pricing (Nakamura and Steinsson (2011)). Second, I do not

explicitly model production of the advertised good. I assume that the advertised good is always

available for firms to buy and re-sell to households at the price of purchase once a firm finds a custo-

mer. This allows to reduce the state space and focus on the implications of advertising externalities

for return predictability. Finally, the model features convex advertising costs to reduce the volatility

of advertising.

As in Liu et al. (2009) and Kuehn et al. (2012), the firm’s problem at time t is to maximize the discoun-

ted expected value of its dividend stream St, subject to the law of motion for its customer base and

3.3. MODEL 87

a non-negativity constraint on advertising. Let Pt denote the period-t relative price of the advertised

good in terms of the numeraire. The representative firm’s problem is

St = max{ADt+j}∞

j=0

Et

∞

∑j=0

Mt+j

Pt+j −χ

2

(ADt+j

Nt+j

)2Nt+j, (3.5)

subject to, for all j,

ADt+j ≥ 0 (3.6)

and the law of motion (3.3). Here, Mt+j denotes the stochastic discount factor (SDF) between t and

t + j, χ is a convex adjustment cost parameter and (3.6) is a non-negativity constraint on effort. Since

the matching probability λt is greater than zero, (3.6) can be re-written as

λt+j ADt+j ≥ 0. (3.7)

Substituting the first constraint into (3.5), and respectively denoting by µnt and µλ

t the time-t Lagrange

multipliers on (3.3) and (3.7), the problem’s first order conditions are

µnt =

χ

λt

ADt

Nt− µλ

t , (3.8)

µnt = Et Mt+1

[Pt+1 +

χ

2

(ADt+1

Nt+1

)2+ (1− ϕ) µn

t+1

], (3.9)

plus the Kuhn-Tucker conditions on (3.3) and (3.7). The Euler equation for customer capital accumu-

lation is therefore

χ

λt

ADt

Nt− µn

t = Et Mt+1

[Pt+1 +

χ

2

(ADt+1

Nt+1

)2+ (1− ϕ)

(χ

λt+1

ADt+1

Nt+1− µn

t+1

)]. (3.10)

The Euler equation relates the marginal cost of adding one unit of search effort at time t to the mar-

ginal benefit in period t + 1 of having λt additional customers, in turn consisting of higher revenues,

lower adjustment costs, higher servicing costs and the discounted marginal cost of postponing to


period t + 1 the unit increase in advertising. Note that at the optimum

St = Et

∞

∑j=0

Mt+j

[Pt+jNt+j −

χ

2

AD2t+j

Nt+j− κNt+j (3.11)

+ µnt+j((1− ϕ) Nt+j + λt+j ADt+j − Nt+j+1

)+ µλ

t+jλt+j ADt+j

],

so that expanding St, I get

St = PtNt −χ

2AD2

tNt− κNt + µn

t ((1− ϕ) Nt + λt ADt − Nt+1) + µλt λt ADt

+ Et Mt+1

[Pt+1Nt+1 −

χ

2AD2

t+1Nt+1

− κNt+1 (3.12)

+ µnt ((1− ϕ) Nt+1 + λt+1ADt+1 − Nt+2) + µλ

t+1λt+1ADt+1 + . . .]

. (3.13)

Recursively substituting (3.10) into (3.12) the equilibrium, cum-dividend price of equity is

St =

(Pt +

χ

2

(ADt

Nt

)2+ (1− ϕ) µn

t

)Nt, (3.14)

and the ex-dividend stock price denoted by St is equal to

St = µnt Nt+1. (3.15)

Finally note that whenever (3.6) does not bind at time t (i.e., advertising is positive) the return of one

unit of advertising is equal to the return on equity Rt+1 between t and t + 1, and is given by

Rt+1 =St+1

St(3.16)

=1

µnt

(Pt+1 +

χ

2

(ADt+1

Nt+1

)2+ (1− ϕ) µn

t+1

)(3.17)

The return on equity, as in Cochrane (1991), is the trade-off between the marginal benefit of posting

an additional ad in period t - accrued between period t and t + 1 - and the ad cost incurred in period

t. Note that for a given level of past advertising, high current advertising and therefore high cur-

rent advertising growth reduce future expected returns. This happens because i) through the goods

market friction high advertising reduces the probability that an additional ad will turn into a custo-

3.3. MODEL 89

mer (from (3.8), µn is decreasing in λ) and ii) high current advertising (and future customer capital)

reduces future marginal revenues.

3.3.2 Household Problem

The household derives its period utility from a bundle of the numeraire good and the advertised

good, and decides how much of its endowment to allocate to consumption, investment in a claim to

firm profits and investment in a risk-free bond. Denote by C0 and C1 the representative household’s

consumption of the numeraire and advertised goods, respectively. Further denote by Y the endo-

wment of the numeraire good, by φ the household investment in claims to the firm profits, and by

θ the household investment in a risk-free asset with current price of one and gross return R f . The

claims to firm profits and the risk-free assets are in unit and zero aggregate net supply, respectively.

The household’s budget constraint at time t + j is therefore

C0,t+j ≤ Yt+j + φt+j−1St+j + θt+j−1R ft+j − Pt+jC1,t+j − φt+jSt+j − θt+j. (3.18)

Moreover, I assume that each firm customer consumes only one unit of the advertised good, so that

C1,t+j ≤ Nt+j. The household’s intraperiod utility is given by the CES function

u (C0; C1) =

((1− α)C

η−1η

0 + αCη−1

η

1

) ηη−1

, (3.19)

where α ∈ [0, 1], and η ≥ 0 is the elasticity of substitution between the numeraire and manufactu-

red goods. Finally, the household’s intertemporal utility is denoted by Vt, and is specified by the

recursion

Vt =

{(1− β) u (C0,t; C1,t)

1− 1ψ + βEt

[V1−γ

t+1

] 1−1/ψ1−γ

} 11−1/ψ

, (3.20)

where β is the time discount factor, ψ is the elasticity of intertemporal substitution, and γ is the

relative risk aversion coefficient (Kreps and Porteus (1978), Epstein and Zin (1989)). The relative


price of C1 is the marginal rate of substitution between C0 and C1, or

P =α

1− α

(C1

C0

)− 1η

. (3.21)

In Appendix C.3 I show that the stochastic discount factor is

Mt+1 = β

(C0,t+1

C0,t

)− 1η(

u (C0,t+1; C1,t+1)

u (C0,t; C1,t)

) 1η−

1ψ

Vt+1

Et

(V1−γ

t+1

) 11−γ

1ψ−γ

. (3.22)

Note that, for a fixed level of past advertising, high current advertising and therefore high current

advertising growth increase customer capital, decrease the numeraire good’s consumption, and in-

crease the stochastic discount factor. This and the fact that future expected returns (3.16) are decrea-

sing in advertising growth implies that high advertising growth generates high negative co-variation

between the stochastic discount factor and expected excess returns, and therefore high risk premia.

Finally, the risk-free rate is

R ft+1 =

1Et [Mt+1]

. (3.23)

3.3.3 Equilibrium

For each combination of the state variables (Y; N), a competitive equilibrium of search in the goods

market specifies policy functions for firm advertising AD (Y; N); policy functions for household

numeraire consumption C0 (Y; N), stock holdings φ (Y; N) and risk-free asset holdings θ (Y; N); a

stock price S (Y; N), a risk-free rate R f (Y; N) and a relative price of the manufactured good in terms

of the numeraire P (Y; N), such that firms and households maximize their constrained objectives,

markets for the numeraire and the advertised goods clear, and aggregate stock and bond markets

clear. In particular, note that the equilibrium conditions in the goods market imply that

C0 = Y− χ

2

(ADN

)2N, (3.24)

and C1 = N.

3.4. RESULTS 91

3.4 Results

Section 3.4.1 describes my calibration strategy and solution method. Section 3.4.2 compares the pre-

dictability results coming from simulations of the model to those coming from post-war US data.

Finally, section 3.4.3 highlights the quantitative importance of goods market frictions in obtaining

the predictability results.

3.4.1 Calibration and Computation

I calibrate the model at an annual frequency. In my calibration strategy I do not try to match the

equity returns predictive regression coefficients found in the data, but rather show that the sign,

magnitude and statistical significance of these coefficients arise naturally when the model is calibra-

ted to match other data moments. Broda and Weinstein (2010) report a median annualized entry

rate of new goods in consumer baskets equal to 0.25. When normalizing household search effort to

unit, this entry rate in the model is equal to(1 + AD−ϑ

)−1/ϑ, which I target to a steady-state value of

0.30 with a matching function elasticity ϑ = 0.57. Finally, the results are not sensitive to the convex

adjustment cost parameter χ, which I therefore set equal to one. On the household side, Petrosky-

Nadeau and Wasmer (2015) document that average annual expenditures on food consumed at home,

plus utilities, amount to 10-15 percent of total annual expenditures in the 1984-2009 Household Con-

sumption Expenditure Survey. I target this share in the model to 17 percent with a bias parameter α

equal to 0.79. I use an AR(1) process in logs to describe the time-series evolution of the numeraire

good’s endowment, and set the persistence and volatility of the endowment process equal to 0.75

and 0.13, respectively. Finally, I set the relative risk aversion coefficient γ equal to 21. The last three

parameters target a equity premium of three percent, a equity premium volatility of twelve percent

and a consumption growth volatility of 1.8 percent while retaining the main predictability results.

I borrow the remaining parameters from the literature. I choose a customer capital depreciation

rate ϕ equal to 0.20 as in Gourio and Rudanko (2014), in the mid-range of the empirical estimates

of Bronnenberg et al. (2012) and in the low range of the estimates of Broda and Weinstein (2010).


Modeling household preferences, I set the annual discount rate β to 0.95, and the intertemporal

elasticity of substitution ψ to 1.5 following Bansal and Yaron (2004). Finally, I set the elasticity of

substitution parameter η equal to 0.83 following the international trade literature (Heathcote and

Perri (2002), Bianchi (2009) and Huo and Rıos-Rull (2013)).

The model is challenging to solve numerically. First, the equilibrium allocations are not Pareto-

optimal. A social planner confronted with the constrained equity maximization problem (3.5) would

in fact internalize the congestion effect created by search effort, while individual firms do not. This in

turn requires solving the model using its first-order conditions. Second, the non-negativity constraint

on search effort renders perturbation methods not suited for this type of problems. For these reasons,

I solve for the competitive search equilibrium using the globally nonlinear computational algorithm

of Petrosky-Nadeau and Zhang (2017). In particular, for each point in the aggregate endowment-

customer capital state space (Yt, Nt), the algorithm solves for optimal advertising AD∗t = AD (Yt, Nt)

and the multiplier on its non-negativity constraint µn∗t = µn (Yt, Nt) from the Euler equation

χ

λt

ADt

Nt− µn (Yt, Nt) = Et Mt+1

[Pt+1 + (1− ϕ)

(χ

λt+1− µn (Yt, Nt)

)], (3.25)

where both λt and Pt are functions of AD (Yt, Nt). Appendix C.4 provides details on the computati-

onal algorithm.

3.4.2 Simulated Moments and Predictability

I simulate ten thousand samples of sixty-one annual observations, and in each simulated sample

compute average advertising and consumption growth, return on equity and risk-free rate. Mo-

reover, in each simulated sample I run predictive regressions of equity returns using consumption

growth and advertising growth as predictors.

Panel A of Table 3.9 reports the average first moment and standard deviation of advertising and con-

sumption growth, equity premium and risk-free rate across the simulated samples. Panel B reports

the corresponding moments in post-war US data. The calibration of the model allows to reasonably

3.4. RESULTS 93

Table 3.9

Model-Simulated Moments

Panel A: Model Panel B: DataMean St. Dev Mean St. Dev

∆a 0.026 0.237 0.023 0.056∆c 0.001 0.021 0.022 0.018

R− R f 0.052 0.173 0.066 0.164R f 0.003 0.056 0.017 0.027

match the first moments of the selected variables, and to match the volatility of consumption growth,

equity premium and risk-free rate.

Table 3.10 tests the predictive power of advertising and consumption growth on future equity re-

turns. As in the data, neither advertising nor consumption growth can alone predict future returns

in the model. Moreover, Conditional on consumption growth, advertising growth however signi-

ficantly predicts future returns. The predictive power of advertising (and consumption) is higher

at longer horizons, and the economic magnitude of the coefficients is close their empirical counter-

parts. As in the data, advertising positively predicts consumption growth and is therefore a priced

aggregate risk factor. Through customer capital, in fact, advertising growth determines growth in

consumption of the manufactured good and increases the numeraire goods’ future marginal utility.

At the same time, advertising growth reduces expected returns to investing in claims to customer

capital. These conditions imply that times when firms spend more resources in advertising are times

of low expected returns and high expected marginal utility, and therefore high risk premia.

3.4.3 The Quantitative Impact of Goods Market Frictions

In this section, I use the insights of the model to explore the effect of goods market frictions on

predictability. In particular, I show that the congestion effect created by aggregate advertising is

quantitatively important in driving both consumption and returns predictability.


Table 3.10

Results: Returns Predictability

The Table shows coefficient estimates for cumulative returns (rt→t+τ) predictive regressions coming from mo-del simulations (Panel A) and from post-war data (Panel B) using lagged advertising expenditures growth(∆at−1→t) and consumption growth (∆ct−1→t) as predictors. The t-statistics in parentheses are computed usingHansen and Hodrick (1980) standard errors.

Panel A: Model Panel B: Data (Post-War)rt→t+1 rt→t+2 rt→t+3 rt→t+4 rt→t+1 rt→t+2 rt→t+3 rt→t+4

(1) ∆at−1→t -0.084 -0.144 -0.219 -0.263 0.358 0.636 1.273 1.385(-0.67) (-1.33) (-1.65) (-1.67) (0.94) (0.96) (1.38) (1.13)

R2adj 0.027 0.030 0.037 0.038 -0.003 0.003 0.031 0.016

(2) ∆ct−1→t -0.103 -0.179 -0.270 -0.326 -2.189 -3.410 -4.121 -6.843(-1.11) (-1.42) (-1.74) (-1.75) (-1.94) (-1.81) (-1.64) (-2.12)

R2adj 0.028 0.032 0.040 0.041 0.042 0.045 0.038 0.065

(3) ∆at−1→t 4.334 8.512 12.198 15.543 1.332 2.204 3.492 4.644(1.83) (1.92) (2.13) (2.20) (3.24) (3.24) (3.57) (3.51)

∆ct−1→t -5.071 -9.934 -14.242 -18.126 -4.712 -7.583 -10.731 -16.174(-1.46) (-1.95) (-2.16) (-2.23) (-3.66) (-3.69) (-3.82) (-4.16)

R2adj 0.069 0.103 0.132 0.149 0.150 0.175 0.246 0.277

3.4. RESULTS 95

Figure 3.5

Customer Capital Investment

The Figure compares the optimal customer capital investment λE in the decentralized economy with the in-vestment in the decentralized economy. Panel A shows the investment as a function of customer capital N,for the lowest possible realization of the endowment process Y. Panel B shows the investment as a function ofcustomer capital N, for the highest possible realization of the endowment process Y.

0.5 1 1.5 2 2.5 3 3.5 40.1

0.2

0.3

0.4Panel A: Low Endowment

DecentralizedCentralized

Customers0.5 1 1.5 2 2.5 3 3.5 4

0.1

0.2

0.3

0.4

0.5Panel B: High Endowment

DecentralizedCentralized

As noted before, the equilibrium allocation in the decentralized economy is not Pareto-optimal. To

solve for the Pareto-optimal allocation, I keep the same steady-state parametrization of the model

described in section 3.4.1 and solve the constrained optimization problem (3.5) using standard value

function iteration. Since firms in the centralized economy do not over-advertise to compensate the

congestion effect created by aggregate advertising, the optimal amount of firm search effort in the

centralized economy is as much as ten times lower than in the decentralized economy. Figure 3.5

shows that as a consequence the effective firm investment in customer capital, λE, is low and almost

flat.

Table 3.11 reports estimates of the same predictive regressions coefficients of Tables (??) and (3.10)


Table 3.11

Predictability in the Centralized Economy

The Table shows coefficient estimates for cumulative consumption growth (∆ct→t+τ) and returns (rt→t+τ) pre-dictive regressions coming from simulations of the centralized economy, using lagged advertising expendi-tures growth (∆at−1→t) and consumption growth (∆ct−1→t) as predictors. The t-statistics in parentheses arecomputed using Hansen and Hodrick (1980) standard errors.

Panel A: Consumption Panel B: Returns∆ct→t+1 ∆ct→t+2 ∆ct→t+3 ∆ct→t+4 rt→t+1 rt→t+2 rt→t+3 rt→t+4

(1) ∆at−1→t -0.116 -0.228 -0.325 -0.378 -0.121 -0.213 -0.326 -0.403(-1.00) (-1.51) (-1.86) (-1.90) (-1.10) (-1.41) (-1.64) (-1.82)

R2adj 0.024 0.033 0.042 0.043 0.024 0.027 0.035 0.039

(2) ∆ct−1→t -0.100 -0.197 -0.278 -0.327 -0.103 -0.184 -0.282 -0.350(-1.00) (-1.80) (-1.89) (-2.00) (-1.04) (-1.30) (-1.74) (-1.92)

R2adj 0.025 0.035 0.045 0.048 0.025 0.030 0.038 0.042

(3) ∆at−1→t 0.159 0.343 0.385 0.552 0.113 0.293 0.398 0.597(0.24) (0.42) (0.53) (0.44) (0.15) (0.32) (0.45) (0.43)

∆ct−1→t -0.219 -0.463 -0.581 -0.765 -0.186 -0.405 -0.588 -0.820(-0.40) (-0.84) (-0.87) (-0.84) (-0.32) (-0.54) (-0.69) (-0.89)

R2adj 0.041 0.047 0.054 0.058 0.041 0.041 0.050 0.054

for the centralized economy. The results show that the volatility of advertising in the decentralized

economy has key implications for predictability. On the consumption predictability side companies

do not over-advertise in the centralized economy, customer capital growth is flat and current ad-

vertising growth does not generate large movements in future customer capital and consumption.

On the returns predictability side, a flat effective investment in customer capital (λE) reduces the

large shifts in marginal profits and marginal utility due to over-advertising, thus reducing the risk

associated with advertising and the predictive power of advertising on future returns.

3.5 Conclusion

In this paper, I provide new evidence on the importance of advertising and goods market frictions

for financial economics. I show that advertising growth predicts future consumption growth in post-

3.5. CONCLUSION 97

war US data, and use this result to verify the core prediction of dynamic asset pricing theory that

expected consumption matters for expected returns. Using advertising and consumption growth to

predict excess returns on equity I show that advertising positively predicts excess returns at horizons

of up to four years. Motivated by these empirical findings, I build a general equilibrium model of

frictional goods markets where advertising is an investment in long-lasting customer relationships

that affect the dynamics of household consumption. The calibrated model is able to replicate the

predictive power of advertising growth on future consumption growth and equity returns observed

in the data, and highlights the importance of frictions in the goods market to quantitatively match

these predictability patterns.

The paper is part of a small literature in financial economics highlighting the importance of adverti-

sing and goods market frictions at the firm level (Gourio and Rudanko (2014), Vitorino (2014)). In this

paper, I show that goods market frictions are also quantitatively relevant in the aggregate. As such,

future research should be devoted to further studying the aggregate implications (i.e. the trade-off

between customer capital and other forms of tangible and intangible capital) and the welfare impact

of these frictions.

Appendix A

Appendix to Chapter 1

99

100 APPENDIX A. APPENDIX TO CHAPTER 1

A.1 Solving for the Optimal Contract

Substituting the manager’s first incentive-compatibility (1.5) constraint into (1.2)-(1.4), the problem

becomes finding m (y) and π1 (y) to maximize

L =∫ y

¯y[P−m (y) (P− π1 (y) + k)] dF (y)− I + ω

∫ y

¯y[y− P + m (y) (P− π1 (y))] dF (y)

+∫ y

¯y[µ (y) [y− P + m (y) (P− π1 (y))] + λ (y) [P−m (y)π1 (y)]] dy, (A.1)

where ω, µ (y), and λ (y) respectively denote the multipliers on (1.3), (1.4), and (1.6). Taking first-

order conditions of (A.1) with respect to m (y) yields

∂L∂m (y)

= [P− π1 (y)] [(ω− 1) f (y) + µ (y)]− k f (y)− λ (y)π1 (y) . (A.2)

If m (y) = 1, it must be that ∂L/∂m (y) > 0.A.1 Therefore,

[P− π1 (y)] [(ω− 1) f (y) + µ (y)] > k f (y) + λ (y)π1 (y) ≥ 0. (A.3)

This implies that R− π1(y) > 0 and λ∗ (y) = 0. On the other hand,

∂L∂π1 (y)

= f (y) (1−ω)− µ (y) , (A.4)

implying that to satisfy ∂L/∂π1 (y) ≥ 0, ω∗ ≤ 1. Then from (A.3), µ (y) > 0 and the limited-liability

constraint must bind such that in the monitoring region π1 (y) = y.

A.1For a given y, if m (y) = 1 it must be that (L (m (y) = 1)−L (m (y) = 0)) /(1− 0) > 0.

A.2. ADDITIONAL RESULTS: BANK VALUE 101

A.2 Additional Results: Bank Value

Table A1

Robustness and Placebo Tests: Market-to-Book

This table reports sample bandwidth selection tests (Panel A) and placebo tests (Panel B) on my main Market-to-Book result. In the first four specifications of Panel A, I use two small samples of BHCs with average 2005total assets between $400 and $600 million (Specifications (1) and (2)), and between $300 and $700 million(Specifications (3) and (4)). In the last four specifications I use two large samples of BHCs with total assetsbetween $150 million and $1 billion (Specifications (5) and (6)), and between $150 million and $1.5 billion(Specifications (7) and (8)). In the first six specifications of Panel B, I use asset thresholds of $300 million, $750million and $1 billion to separate treated and control BHCs. In Specifications (7) and (8) I use the last quarterof 2004 as treatment quarter, dropping post-2005 observations from the sample. In the last two specifications,I use the last quarter of 2006 as treatment quarter. The dependent variable in all specifications is the naturallogarithm of Tobin’s q. Unreported control variables include leverage, Tier 1 Ratio, total assets, profitability,ROE, diversification, and asset growth.

Panel A: Sample Bandwidth Selection

$400M-600M $300M-700M $150M-1B $150M-1.5B

(1) (2) (3) (4) (5) (6) (7) (8)

Post × Treated -0.087** -0.088** -0.055** -0.072*** -0.052** -0.073*** -0.055*** -0.075***(0.04) (0.03) (0.03) (0.02) (0.02) (0.02) (0.02) (0.02)


Year-Quarter FE Yes Yes Yes Yes Yes Yes Yes YesBHC FE Yes Yes Yes Yes Yes Yes Yes YesR-Squared 0.149 0.338 0.106 0.296 0.068 0.250 0.055 0.215Observations 355 355 724 724 1,313 1,313 1,611 1,611

Panel B: Placebo Tests

$300M Threshold $750M Threshold $1B Threshold After 12/2004 After 12/2006

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Post × Treated -0.03 -0.04 0.01 -0.00 0.03 0.01 -0.01 -0.00 -0.04 -0.04*(0.04) (0.04) (0.03) (0.03) (0.03) (0.03) (0.02) (0.02) (0.03) (0.02)





Table A2

Bank Size Manipulation Tests

This table shows point estimates (and associated t-statistics) of discontinuities in the cross-sectional density ofbank assets around the $500 million policy implementation threshold. The smoothed density is obtained byfirst constructing a finely-gridded histogram of BHC total assets and then smoothing the histogram on eachsize of the threshold using local linear regression. The reported tests are then Wald tests of the null hypothesisthat the log difference in the smoothed density above and below the threshold is zero. The optimal histogrambin size and local linear regression bandwidth are calculated as in McCrary (2008).

2005-2007 Sample 2005 Sample 2006-2007 Sample

Discontinuity Estimate 0.0737 0.110 0.0379t-stat 0.674 0.522 0.330Observations 2,039 692 1,347

Table A3

Event Study Around Policy Date

In this table I report the results of an event study around the Fed policy date (March 6, 2006). For each bank inmy sample, in the second half of 2005 I estimate the market model by regressing daily bank stock returns on aconstant and the daily CRSP value-weighted index. I then use the estimated coefficients to compute abnormalstock returns (the difference between actual returns and market-model-predicted returns) around the eventdate. I choose a symmetric event window starting two weeks before and ending two weeks after the event dayweek. Next, I compute daily average abnormal returns in the treated and control groups, and then computegroup-level Cumulative Abnormal Returns (CARs) as the sum of these daily average abnormal returns withinthe event window. I finally compute the t-statistics for the null hypothesis that CAR is zero as the ratio betweenCAR and the standard deviation of average abnormal returns, normalized by the inverse of the square root ofthe number of days in the event window (see, for example, Corrado (2011)). In the last two columns of thetable, I repeat the same exercise using weekly returns instead of daily returns.

Daily Frequency Weekly Frequency

Treated Control Treated Control

Cumulative Abnormal Return -0.0180 0.00264 -0.0139 0.00725t-stat -2.144 0.277 -3.315 1.189Observations (Event Window) 24 24 5 5


Table A4

Additional Robustness

This table provides robustness tests for the main results in Table 1.2 using different restrictions on the mainsample. In the first two specifications, I restrict the sample to the years 2005 and 2006. In Specifications (3)and (4), I extend the sample to include the financial crisis. In Specifications (5) and (6) I only include survivorBHC (BHCs whose data is available for the entire 2004-2007 period). In Specifications (7) and (8), I drop banksthat get listed on the stock market after the treatment. The dependent variables are the natural logarithm ofTobin’s q (Panel A) and Market-to-Book (Panel B). Unreported control variables include leverage, Tier 1 Ratio,profitability, ROE, diversification, and asset growth.

Panel A: log Tobin’s q Regressions

2005-2006 Sample 2004-2008 Sample Survivors Only Listed in 2005

(1) (2) (3) (4) (5) (6) (7) (8)

Post × Treated -0.013*** -0.014*** -0.008** -0.008** -0.008* -0.010** -0.010*** -0.010***(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)


Year-Quarter FE Yes Yes Yes Yes Yes Yes Yes YesBHC FE Yes Yes Yes Yes Yes Yes Yes YesR-Squared 0.078 0.128 0.630 0.679 0.370 0.419 0.351 0.412Observations 1,113 1,113 2,711 2,711 1,518 1,518 2,103 2,103

Panel B: log Market-to-Book Regressions

2005-2006 Sample 2004-2008 Sample Survivors Only Listed in 2005

(1) (2) (3) (4) (5) (6) (7) (8)

Post × Treated -0.074*** -0.089*** -0.070** -0.072*** -0.056* -0.069** -0.069*** -0.075***(0.02) (0.02) (0.03) (0.03) (0.03) (0.03) (0.03) (0.02)


Year-Quarter FE Yes Yes Yes Yes Yes Yes Yes YesBHC FE Yes Yes Yes Yes Yes Yes Yes YesR-Squared 0.086 0.251 0.647 0.710 0.428 0.514 0.404 0.503Observations 1,113 1,113 2,711 2,711 1,518 1,518 2,103 2,103



Table A5

Quarterly Treatment Effects

This table provides quarterly estimates of the treatment effect on bank value. The table is identical to Table 1.2,but here I assign an individual indicator to each post-treatment quarter. For example, the “Q1-2006× Treated”indicator identifies observations for treated banks in the first quarter of 2006. All the variables are defined asin Table 1.1.


(1) (2) (3) (4) (5) (6)

Q1-2006 × Treated -0.009** -0.010*** -0.010** -0.057** -0.065*** -0.060***(0.00) (0.00) (0.00) (0.02) (0.02) (0.02)

Q2-2006 × Treated -0.011*** -0.012*** -0.011*** -0.069** -0.078*** -0.073***(0.00) (0.00) (0.00) (0.03) (0.03) (0.03)

Q3-2006 × Treated -0.012*** -0.013*** -0.013*** -0.079*** -0.089*** -0.084***(0.00) (0.00) (0.00) (0.03) (0.03) (0.03)

Q4-2006 × Treated -0.013*** -0.013*** -0.013*** -0.073** -0.082*** -0.077***(0.00) (0.00) (0.00) (0.03) (0.03) (0.03)

Q1-2007 × Treated -0.009** -0.010** -0.009** -0.065** -0.073** -0.068**(0.00) (0.00) (0.00) (0.03) (0.03) (0.03)

Q2-2007 × Treated -0.008 -0.009** -0.009** -0.064* -0.079** -0.075**(0.00) (0.00) (0.00) (0.04) (0.03) (0.03)

Q3-2007 × Treated -0.009* -0.009* -0.009* -0.073* -0.081** -0.074**(0.00) (0.00) (0.00) (0.04) (0.03) (0.03)

Q4-2007 × Treated -0.007 -0.008 -0.008 -0.077* -0.086** -0.079**(0.01) (0.01) (0.01) (0.05) (0.04) (0.04)

Leverage 0.318*** 0.254** 5.475*** 5.170***(0.12) (0.10) (0.81) (0.68)

Tier 1 Ratio 0.376*** 0.280*** 2.540*** 1.747***(0.08) (0.07) (0.51) (0.48)





Table A6

Falsification Tests: Non-Fed-Regulated Firms

In this table, I study whether firms that are not regulated by the Fed experience a valuation discount at thebeginning of 2006. I first merge quarterly Compustat with the Fed Bank Regulatory dataset to identify andremove BHCs from the sample. I then identify non-BHC financial firms as firms with CRSP SIC code between6000 and 6799. Finally, I remove observations of firms with less than $400 million and more than $600 millionin 2005 average total assets, and use a $500 million asset threshold to classify firms as “small” (average 2005assets below the threshold) and “large” (average 2005 assets above the threshold). In Panel A, I investigatevaluation changes in the falsification sample of non-financial firms. In Panel B, I investigate valuation chan-ges in the sample of non-BHC financial firms. Unreported control variables include leverage (book value ofdebt divided by book value of equity), quarterly operating investment (percentage change in quarterly ope-rating assets, where operating assets are the sum of PP&E, trade receivables net of trade payables, deferredtaxes and investment tax credit, and other current assets), interest coverage (operating income before depreci-ation divided by interest expense), profitability (operating income divided by revenues), and Return on Assets(operating income divided by total assets).

Panel A: Non-Financials


(1) (2) (3) (4) (5) (6)

Post × Small Non-Fin. -0.026 -0.042 -0.046 0.066 0.050 0.041(0.05) (0.05) (0.04) (0.08) (0.08) (0.07)

log Assets -0.185*** -0.197*** -0.288*** -0.304***(0.05) (0.04) (0.08) (0.08)


Year-Quarter FE Yes Yes Yes Yes Yes YesFirm FE Yes Yes Yes Yes Yes YesR-Squared 0.161 0.190 0.225 0.139 0.165 0.226Observations 3,459 3,459 3,459 3,268 3,268 3,268

Panel B: Non-BHC Financials


(1) (2) (3) (4) (5) (6)

Post × Small Non-BHC 0.109 0.040 -0.032 0.131 0.112 0.040(0.20) (0.19) (0.15) (0.20) (0.18) (0.15)

log Assets -0.383* -0.415* -0.105 -0.164(0.20) (0.20) (0.18) (0.17)


Year-Quarter FE Yes Yes Yes Yes Yes YesFirm FE Yes Yes Yes Yes Yes YesR-Squared 0.231 0.337 0.508 0.310 0.314 0.558Observations 299 299 299 299 299 299



A.3 Additional Results: Management Monitoring

Table A7

Triple Differences: Policy Effect on Market-to-Book

In this table I investigate whether the negative correlation between post-treatment professional expendituregrowth and value discounts is mechanically driven by changes in other variables that are correlated withprofessional expenditures. In practice, I repeat the same exercise as in Table 1.5 but interacting the “Post ×Treated” indicator with ROE, total assets and Z-Score.

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Post × Treated (a) -0.072*** -0.071*** -0.084*** -0.072*** -0.069*** 0.940 -0.072*** -0.073*** -0.065**(0.03) (0.03) (0.03) (0.03) (0.03) (0.72) (0.03) (0.03) (0.03)

ROE (b) 0.689** 0.294(0.33) (0.42)

(a) × (b) 0.654*(0.34)

log Assets (c) -0.282*** -0.261***(0.06) (0.06)

(a) × (c) -0.078(0.06)

Z-Score (d) 0.000 0.000(0.00) (0.00)

(a) × (d) -0.000*(0.00)

Year-Quarter FE Yes Yes Yes Yes Yes Yes Yes Yes YesBHC FE Yes Yes Yes Yes Yes Yes Yes Yes YesR-Squared 0.368 0.377 0.380 0.368 0.403 0.406 0.368 0.376 0.377Observations 2,623 2,623 2,623 2,623 2,623 2,623 2,623 2,516 2,516


A.3. ADDITIONAL RESULTS: MANAGEMENT MONITORING 107

Table A8

Audit Fees

In this table, I show the treatment effect on different components of bank professional expenditure, and inparticular on audit fees. The data comes from annual AuditAnalytics (AA). In Panel A, I show the treatmenteffect on AuditAnalytics audit fees, non-audit fees (the sum of employee benefit plan audits, due diligenceand accounting related to mergers and acquisitions, internal control reviews, and other fees) and the differencebetween annual professional fees from Compustat and total annual fees (sum of audit and non-audit fees) fromAuditAnalytics. In Panel B, I scale the variables by annual net income from Compustat. Unreported controlvariables include annual leverage, Tier 1 Ratio, total assets, ROE, and diversification, defined as in Table 1.1.

Panel A: log Fees

AA Audit Fees AA Non-Audit Fees Residual Prof. Fees

(1) (2) (3) (4) (5) (6)

Post × Treated -0.029 -0.019 0.197* 0.207* 1.425*** 1.306***(0.05) (0.05) (0.11) (0.11) (0.35) (0.34)



Panel B: log Fees-to-Net Income

AA Audit Fees AA Non-Audit Fees Residual Prof. Fees

(1) (2) (3) (4) (5) (6)

Post × Treated -0.009 0.057 0.186 0.262** 1.316*** 1.135***(0.10) (0.07) (0.15) (0.13) (0.38) (0.42)





Table A9

Internal Controls and Post-Treatment Professional Expenditure

In this table I study the interaction between internal controls and professional expenditure. I assign treatedbanks to one of two groups based on whether they mention (the Internal Controls (IC) group) or they do notmention (the No-IC group) internal controls as a source of professional expenditure in the notes to their 2006and 2007 10-K filings. The table provides an estimate of the treatment effect on professional expenditure inthese two groups. Unreported control variables include total assets, profitability, ROE, diversification, andasset growth.

log Professional Fees log Professional FeesNet Interest Revenue

(1) (2) (3) (4) (5) (6)

Post × Treated × No-IC 0.059 0.057 0.105 0.086 0.083 0.087(0.09) (0.09) (0.08) (0.10) (0.10) (0.09)

Post × Treated × IC 0.403*** 0.422*** 0.331*** 0.337*** 0.337*** 0.326***(0.11) (0.10) (0.09) (0.11) (0.11) (0.09)

Leverage -1.981 -1.415 2.187 0.911(3.12) (2.45) (3.10) (2.58)

Tier 1 Ratio -4.557*** -2.467* -1.431 -1.576(1.51) (1.35) (1.52) (1.43)

Controls No No Yes No No Yes




Table A10

SEC Accelerated Filers

In this table, I investigate whether the observed changes in valuation and professional expenses after the tre-atment are due to size-related SOX provisions as opposed to the Fed policy. Similar to Iliev (2010), in Panel A Irun a falsification test to investigate whether SEC resolution 70 FR 56825 (allowing small, non-accelerated SECfilers to postpone the implementation of SOX) has a valuation impact on non-accelerated SEC filers after thefirst quarter of 2006. In Panel B, I similarly investigate whether the treatment effect on professional fees comesfrom the subset of treated BHCs that are non-accelerated filers. Unreported control variables include leverage,Tier 1 Ratio, profitability, ROE, diversification, and asset growth.

Panel A: Accelerated Filers vs. Non-Accelerated Filers

log Tobin’s q log Market-to-Book log Prof. Fees log Prof. FeesNet Int. Income

(1) (2) (3) (4) (5) (6) (7) (8)

Post × Nonacc. Filer -0.004 -0.005 -0.021 -0.036 0.128 0.111 0.108 0.118(0.00) (0.00) (0.02) (0.02) (0.08) (0.08) (0.09) (0.08)


Year-Quarter FE Yes Yes Yes Yes Yes Yes Yes YesBHC FE Yes Yes Yes Yes Yes Yes Yes YesR-Squared 0.039 0.090 0.061 0.217 0.031 0.077 0.043 0.106Observations 985 985 985 985 461 461 461 461

Panel B: Interaction Effects, Treated × Accelerated Filers

log Tobin’s q log Market-to-Book log Prof. Fees log Prof. FeesNet Int. Income

(1) (2) (3) (4) (5) (6) (7) (8)

Post × Nonacc. Treated -0.011*** -0.011*** -0.055** -0.077*** 0.246*** 0.213** 0.207** 0.227***(0.00) (0.00) (0.02) (0.02) (0.08) (0.08) (0.09) (0.08)

Post × Acc. Treated -0.026*** -0.027*** -0.130*** -0.142*** 0.204 0.214 0.225 0.201(0.01) (0.01) (0.05) (0.04) (0.15) (0.15) (0.16) (0.15)


Year-Quarter FE Yes Yes Yes Yes Yes Yes Yes YesBHC FE Yes Yes Yes Yes Yes Yes Yes YesR-Squared 0.099 0.153 0.098 0.262 0.056 0.097 0.062 0.124Observations 1,025 1,025 1,025 1,025 480 480 480 480



Table A11

Summary Statistics: Funding Costs, Profitability, and Earnings Smoothing

This table reports summary statistics for the dependent variables used in Section 1.5.1, both in the 2006-2008full sample and in the two sub-samples of banks with total assets below $500 million and with total assetsbetween $500 and $700 million (the “unmonitored” and “monitored” groups, respectively). In the table, LLPstands for Loan Loss Provisions, while DNLLP stands for Discretionary Negative Loan Loss Provisions (seeTable 1.6). All the variables are constructed using data from quarterly Compustat Bank, and are reported inpercentage terms.

2006-2008 Sample Unmonitored Monitored


Int. Expense/Total Loans 1,129 1.02 0.99 0.32 625 1.01 0.98 0.36 504 1.02 1.00 0.27Int. Income/Total Loans 1,128 2.30 2.21 0.50 625 2.33 2.22 0.59 503 2.25 2.21 0.36ROE 1,067 1.24 1.99 3.89 613 1.01 1.92 3.97 454 1.54 2.13 3.75LLP/Net Interest Income 1,110 0.00 0.00 0.03 612 0.00 0.00 0.03 498 0.00 0.00 0.02DNLLP 1 645 6.55 4.61 6.33 359 6.68 4.64 6.38 286 6.38 4.49 6.28DNLLP 2 651 6.62 4.57 6.33 364 6.70 4.75 6.36 287 6.51 4.41 6.30


Table A12

Funding Costs and Earnings Smoothing: Robustness and Placebo

In this table, I show two sets of robustness test on the results of Table 1.6. In Panel A, I show changes in thefunding costs (interest expense divided by interest income, Specification (1), and interest expense divided bytotal loans, Specification (2)), profitability (ROA and ROE), LLP (LLP to loans, Specification (5), and LLP tonet interest income, Specification (6)), and discretionary LLP (DLLP 1 and 2) of unmonitored banks duringthe financial crisis, where I restrict the sample to banks that survive for the entire 2006-2008 period. In PanelB, I use an alternative threshold of $400 million to define unmonitored banks. Unreported controls includeprevious-quarter Tobin’s q, leverage, Tier 1 Ratio, total assets, diversification, and asset growth in the first fourspecifications of both panels, as well as operating profitability and ROE in the last four specifications.

Panel A: Surviving Banks

Funding Costs ROA/ROE LLP DNLLP

(1) (2) (3) (4) (5) (6) (7) (8)

Crisis × Unmonitored 0.033 0.061** -0.080 -0.088 -0.519*** -0.553** 0.463* 0.619**(0.02) (0.02) (0.10) (0.10) (0.19) (0.22) (0.25) (0.26)

Controls Yes Yes Yes Yes Yes Yes Yes Yes


Panel B: $400M Monitoring Threshold Placebo Sample

Funding Costs ROA/ROE LLP DNLLP

(1) (2) (3) (4) (5) (6) (7) (8)

Crisis × Small 0.011 0.031 -0.140 -0.156 -0.144 -0.078 0.379 0.492(0.02) (0.03) (0.13) (0.13) (0.26) (0.29) (0.27) (0.30)

Controls Yes Yes Yes Yes Yes Yes Yes Yes




Table A13

Robustness: Cash Flow Risk, Shareholder Value, and Professional Expenditure

In this table I perform a robustness check on the results of Table 1.7 by using alternative risk measures to sorttreated banks. In Panel A I sort treated banks based on whether their average Z-Score is above or below themedian Z-Score in my sample. Similarly, in Panel B I sort treated banks based on whether their average equityvolatility is above or below the median equity volatility in my sample. Both Z-Score and equity volatility aredefined as in Table 1.5. Unreported control variables include leverage, Tier 1 Ratio, total assets, profitability,ROE, diversification and asset growth.

Panel A: Z-Score Sorting


(1) (2) (3) (4) (5) (6)

Post × Treated × Low Z-Score -0.008 -0.008* -0.050 -0.058* 0.244* 0.215**(0.00) (0.00) (0.03) (0.03) (0.14) (0.09)

Post × Control × High Z-Score -0.012*** -0.013*** -0.086*** -0.088*** 0.272*** 0.269***(0.00) (0.00) (0.03) (0.03) (0.09) (0.09)



Panel B: Equity Volatility Sorting


(1) (2) (3) (4) (5) (6)

Post × Treated × Low Volatility -0.006 -0.007 -0.027 -0.041 0.320*** 0.267***(0.00) (0.00) (0.03) (0.03) (0.10) (0.09)

Post × Treated × High Volatility -0.012*** -0.013*** -0.095*** -0.094*** 0.212* 0.227***(0.00) (0.00) (0.03) (0.03) (0.12) (0.08)





Table A14

Chairman Ownership and Professional Expenditure Persistence

This table shows the persistence of the treatment effect on professional expenditure for treated banks withchairman ownership in the bottom two terciles of the chairman ownership distribution in my sample, as wellas in the top tercile of the distribution. The independent variable is the natural logarithm of professionalexpenditures. Unreported control variables include leverage, Tier 1 Ratio, total assets, profitability, ROE, di-versification and asset growth.

Low Chairman Own. Treated High Chairman Own. Treated

(1) (2) (3) (4) (5) (6)

Q1-2006 × Treated 0.148 0.160* 0.173* 0.272** 0.293*** 0.238**(0.10) (0.09) (0.09) (0.11) (0.10) (0.09)

Q2-2006 × Treated 0.288** 0.280** 0.290*** 0.395*** 0.404*** 0.314**(0.11) (0.11) (0.11) (0.14) (0.13) (0.12)

Q3-2006 × Treated 0.144 0.153 0.150 0.406*** 0.429*** 0.337***(0.11) (0.10) (0.10) (0.13) (0.13) (0.12)

Q4-2006 × Treated 0.033 0.020 0.027 0.421*** 0.424*** 0.328**(0.12) (0.11) (0.11) (0.16) (0.15) (0.16)

Q1-2007 × Treated 0.210* 0.196* 0.209** 0.484*** 0.486*** 0.389**(0.12) (0.12) (0.10) (0.18) (0.16) (0.16)

Q2-2007 × Treated 0.275** 0.277** 0.265*** 0.511*** 0.531*** 0.414***(0.13) (0.12) (0.10) (0.17) (0.15) (0.13)

Q3-2007 × Treated 0.351** 0.344*** 0.343*** 0.530*** 0.541*** 0.447***(0.14) (0.13) (0.10) (0.18) (0.16) (0.14)

Q4-2007 × Treated 0.198 0.188 0.167 0.338 0.333 0.259(0.20) (0.20) (0.17) (0.27) (0.25) (0.24)

Controls No Yes Yes No Yes Yes




Table A15

Chairman Ownership and Market-to-Book Discount Persistence

This table shows the persistence of the treatment effect on Market-to-Book for treated banks with chairmanownership in the bottom two terciles of the chairman ownership distribution in my sample, as well as in the toptercile of the distribution. The independent variable is the natural logarithm of Market-to-Book. Unreportedcontrol variables include leverage, Tier 1 Ratio, total assets, profitability, ROE, diversification and asset growth.

Low Chairman Own. Treated High Chairman Own. Treated

(1) (2) (3) (4) (5) (6)

Q1-2006 × Treated -0.045* -0.053** -0.051** -0.052* -0.067** -0.056**(0.02) (0.02) (0.02) (0.03) (0.03) (0.03)

Q2-2006 × Treated -0.061** -0.069** -0.068** -0.061* -0.075** -0.064*(0.03) (0.03) (0.03) (0.03) (0.03) (0.03)

Q3-2006 × Treated -0.068** -0.075** -0.076*** -0.075** -0.096*** -0.084**(0.03) (0.03) (0.03) (0.04) (0.03) (0.03)

Q4-2006 × Treated -0.067** -0.069** -0.069** -0.063 -0.085** -0.071*(0.03) (0.03) (0.03) (0.04) (0.04) (0.04)

Q1-2007 × Treated -0.069** -0.072** -0.070** -0.055 -0.075** -0.066*(0.03) (0.03) (0.03) (0.04) (0.04) (0.03)

Q2-2007 × Treated -0.060 -0.070** -0.070** -0.052 -0.082* -0.074*(0.04) (0.04) (0.03) (0.05) (0.05) (0.04)

Q3-2007 × Treated -0.075* -0.075** -0.070** -0.049 -0.082* -0.061(0.04) (0.04) (0.03) (0.05) (0.04) (0.04)

Q4-2007 × Treated -0.094* -0.094** -0.090** -0.059 -0.086 -0.077(0.05) (0.04) (0.04) (0.06) (0.05) (0.05)

Controls No Yes Yes No Yes Yes



A.4. TESTS OF ADDITIONAL HYPOTHESES 115

A.4 Tests of Additional Hypotheses

Table A16

Government Tail Risk Insurance

In this table, I investigate the treatment effect on treated banks’ exposure to bank-specific tail risk (Gandhi andLustig (2015)). In each quarter from Q1-2004 to Q4-2008, I sort commercial bank stocks into five size portfoliosbased on their market capitalization at the end of the previous quarter. I compute daily value-weighted excessreturns on each of the five size portfolios, and regress these daily excess returns on the Fama-French market, hmland smb risk factors (from Kenneth French’s website), and two factors measuring bank interest rate risk (ltg,the yield on a 10-year treasury note minus the yield on a 2-year treasury note) and credit risk (crd, the Moody’sSeasoned Aaa Corporate Bond Yield index minus the yield on a 10-year treasury note). The data used toconstruct ltg and crd comes from the Federal Reserve of St. Louis’ website. I combine the residuals from thetime-series regressions in a (Td × 5) matrix (where Td is the number of daily portfolio return observations forthe period 2004-2007), and obtain the size factor as the second principal component of this matrix. The tableshows the treatment effect on the quarterly loading of each bank’s excess returns on the size risk factor. Theloadings I use as dependent variables in the first three specifications come from the market model augmentedwith the bank size factor, while the loadings in the last three specifications come from the Gandhi-Lustig (GL)specification that includes the bank size factor and the other orthogonal factors (market, hml, smb, ltg and crd)as risk factors. The unreported liquidity controls include all the liquidity variables from Table A18, Panel A.The remaining unreported controls include leverage, Tier 1 Ratio, profitability, ROE, diversification, and assetgrowth.

Factor Loading (Market Model) Factor Loading (GL Model)

(1) (2) (3) (4) (5) (6)

Post × Treated 0.000 0.001 0.000 0.000 0.001 0.000(0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

Liquidity Controls No Yes Yes No Yes Yes





Table A17

Voluntary Reporting

This table compares the treatment effect on Tobin’s q (Panel A) and Market-to-Book (Panel B) across two sub-groups of treated BHCs. The first sub-group consists of treated BHCs that voluntarily file form FR Y-9C afterthe treatment. The second sub-group consists of treated BHCs that stop filing form FR Y-9C after the treatment.Unreported control variables include professional fees, profitability, ROE, diversification, and asset growth.

Panel A: log Tobin’s q Regressions

Voluntary Reporting Not Reporting

(1) (2) (3) (4) (5) (6)

Post × Treated -0.012** -0.012*** -0.012*** -0.010** -0.011*** -0.010***(0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

Leverage 0.395** 0.311** 0.291** 0.211*(0.15) (0.13) (0.13) (0.11)

Tier 1 Ratio 0.489*** 0.366*** 0.293*** 0.184***(0.11) (0.11) (0.07) (0.06)



Panel B: log Market-to-Book Regressions

Voluntary Reporting Not Reporting

(1) (2) (3) (4) (5) (6)

Post × Treated -0.082* -0.089** -0.084** -0.078*** -0.084*** -0.075***(0.04) (0.03) (0.04) (0.03) (0.03) (0.02)

Leverage 5.873*** 5.307*** 5.215*** 4.868***(0.94) (0.88) (0.91) (0.74)

Tier 1 Ratio 3.053*** 2.236*** 2.062*** 1.094**(0.71) (0.73) (0.48) (0.42)




A.4. TESTS OF ADDITIONAL HYPOTHESES 117

Table A18

Liquidity, Volatility, and Market Frictions

In this table, I study the treatment effect on liquidity, volatility, and market information responsiveness oftreated banks’ stocks. In Panel A, I show the treatment effect on the Holden (2009) Effective Tick Size, theCorwin and Schultz (2012) Bid-Ask Spread, and the Amihud (2002) liquidity measures (constructed as in thereferenced papers). Moreover, I show the effect on Zero Days Traded (number of days in which a stock is nottraded) and Turnover (daily volume divided by shares outstanding). Effective Tick Size and Zero Days Tradedare computed on a quarterly basis, while Bid-Ask Spread, Amihud and Turnover are quarterly averages ofdaily measures. In Panel B, I show the treatment effect on quarterly return volatility, quarterly idiosyncraticvolatility (IdVol) from the Fama-French four factor model (FF4), and quarterly idiosyncratic volatility fromthe Adrian et al. (2015) Financial CAPM model (FCAPM). Finally, in Specifications (7)-(10) I show the effecton quarterly measures of price responsiveness to market information (D1 and D2, as in Hou and Moskowitz(2005)). All the variables used in the table are constructed using daily stock returns from CRSP. The controlvariables in Panels A and B include leverage, Tier 1 Ratio, profitability, ROE, diversification, and asset growth.Moreover, Panel B includes all the liquidity variables from Panel A as additional controls.

Panel A: Liquidity

Effective Tick CS Spread Amihud Zero Days Turnover

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Post × Treated -0.000 -0.000 -0.003 -0.003 0.000* 0.000* 0.006 0.001 -0.000 -0.000(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.01) (0.00) (0.00)



Panel B: Equity Volatility and Market Delay

Total Vol FF4 IdVol FCAPM IdVol D1 D2

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Post × Treated -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 0.040* 0.030 0.245 0.222(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.02) (0.02) (0.40) (0.39)

Liquidity Controls No Yes No Yes No Yes No Yes No Yes

Other Controls No Yes No Yes No Yes No Yes No Yes




Table A19

Leverage and Capital Ratios

In this table, I investigate the treatment effect on bank leverage and capital requirements. In Panel A, I investi-gate the treatment effect on three different measures of bank leverage, namely liabilities divided by total assets,divided by the book value of equity and divided by total earning assets (the sum of cash and due from banks,assets sold under repurchase agreements, trading account securities, investment securities, loans net of loanloss allowance, customer acceptances, and other assets). In Panel B, I investigate the treatment effect on theTier 1, Tier 2 and Combined (Tier 1 plus Tier 2) Capital Ratio of treated banks. The Tier 1 Ratio is the sum ofequity capital and minority interests, divided by risk-weighted assets. The Tier 2 Ratio is the sum of cumula-tive preferred stock, qualifying debt, and allowance for credit losses minus investment in certain subsidiaries,divided by risk-weighted assets. Unreported control variables include profitability, ROE, diversification, andasset growth.

Panel A: Leverage

log LiabilitiesAssets log Liabilities

Equity log LiabilitiesEarning Assets

(1) (2) (3) (4) (5) (6)

Post × Treated -0.001 -0.001 -0.009 -0.012 -0.002 -0.002(0.00) (0.00) (0.03) (0.03) (0.00) (0.00)



Panel B: Capital Ratios

log Tier 1 Ratio log Tier 2 Ratio log Combined Ratio

(1) (2) (3) (4) (5) (6)

Post × Treated 0.026 0.033 -0.064 -0.065 0.007 0.013(0.02) (0.02) (0.05) (0.05) (0.02) (0.02)




Appendix B


119

120 APPENDIX B. APPENDIX TO CHAPTER 2

B.1 Substitutability and Price Externalities

In this Appendix extend the analysis of Section 2.3 by allowing for a rich degree of price externa-

lities. In particular, we analyze the degree to which the ability of the Principal to impose group

punishments improves social welfare when varying the degree of substitutability between the out-

put of individual producers. In Section B.1.1, we introduce a new pricing function which admits

a variable degree of substitution across producers’ goods and derive equilibrium outcomes of the

stage game. In Section B.1.2, we develop a recursive formulation of the infinite-horizon game and

show that the usefulness of group punishments increases as goods become more substitutable.

B.1.1 Stage Game

We generalize the price function by assuming that consumers have Cobb-Douglas preferences over

a bundle of individual producers’ output and a numeraire good, and that these consumers face taxes

τ on purchases of each producers’ output. In this economy, the inverse demand function for each

producer i’s output satisfies

pi (q, τ) = αqρ−1

i

∑ni=1 qρ

i− τ, (B.1)

where α ∈ (0, 1) and ρ ∈ (0, 1). Here, the parameter α is a Cobb-Douglas parameter that governs

the substitutability between the numeraire good and the bundle of producers’ output, while the

parameter ρ governs the degree of substitutability between each producer’s output. Under this

formulation, a higher level of ρ implies a higher degree of substitutability.

With prices specified in (B.1), each producer i obtains a static payoff given by

ui (q, τ) = αqρ

i

∑ni=1 qρ

i− τqi − cqi, (B.2)

while the Principal obtains a static payoff given by

w (Q, τ) =n

∑i=1

pi(q, τ)qi (B.3)

= α− τQ. (B.4)

B.1. SUBSTITUTABILITY AND PRICE EXTERNALITIES 121

As in the case of a linear inverse demand function, after observing any level Q, the Principal op-

timally chooses τ (Q) = 0 in the stage game. We impose a restriction on the strategy set of each

producer which requires strictly positive production. Formally, we restrict qi ∈[q, ∞

]with q < qN

i .

Under this restriction, the level of output that maximizes joint profits in the stage game satisfies

qmi = arg max

qi≥q

(α

n− cqi

)(B.5)

= q. (B.6)

Next, to solve for the unique perfect-public equilibrium of the stage game qNi , we note that for each

q−i, producer i solves

maxqi

αqρ

i

qρi + ∑−i qρ

−i− cqi.

It is straightforward to show that the unique perfect-public equilibrium of the stage game is

qNi =

n− 1n2

αρ

c. (B.7)

B.1.2 Infinitely-Repeated Game

We focus on characterizing strongly symmetric perfect-public equilibria. We denote by u (q, τ) the

producer’s payoff and by w (Q, τ) the Principal’s payoff, and after appealing to the one-shot devia-

tion principle, we proceed to characterize the best and worst perfect-public equilibria of the repeated

game. Under the inverse demand function (B.1), for a given level of the worst equilibrium payoff v

the best equilibrium payoff v solves

v = maxq

u (q, 0) ,

subject to, for all q′,

u (q, 0) ≥ (1− δ) g(q′, q, τ

(q′ + (n− 1) q

))+ δv, (B.8)

v ≥ 1− δ

δ

1n[w(q′ + (n− 1) q, 0

)− w

(q′ + (n− 1) q, τ

(q′ + (n− 1) q

))]+ v, (B.9)


where g (q′, q, τ (q′ + (n− 1) q)) now satisfies

g(q′, q, τ

(q′ + (n− 1) q

))= u

(q′, q, τ

(q′ + (n− 1) q

)]+

1n

w(q′ + (n− 1) q, 0

)− 1

nw(q′ + (n− 1) q, τ

(q′ + (n− 1) q

)). (B.10)

As in the previous section, we define the maximum payoff that can be achieved by a producer by

deviating to q′ when the others are producing q as g (q, τ (·)). This maximum payoff satisfies

g (q, τ (·)) = maxq′

g(q′, q, τ(q′ + (n− 1)q)

).

In the next lemma, we show that as long as the prescribed output is larger than the static Nash

equilibrium output, the maximum deviation payoff g(q, τ (·)) is minimized when the Principal levies

no taxes (i.e., when τ = 0).

Lemma 12. g (q, τ (·)) ≥ g (q, τ = 0) when q ≥ qN .


Given Lemma 12, the key propositions of Section 2.3 immediately extend to the environment with

imperfectly substitutable goods. Here, we explore how the usefulness of group punishments in

improving welfare depends on the degree of substitutability between individual producers’ output.

We start by showing in the following lemma that when the number of producers n is sufficiently

large, the best equilibrium level of output of the model where taxes are not allowed is increasing in

the substitutability parameter ρ.

Lemma 13. For n sufficiently large, dqA/dρ > 0.


The intuition behind this lemma is that when output is more substitutable the negative impact of

an individual producer’s output on the common price is lower. This increases producers’ incentives

B.1. SUBSTITUTABILITY AND PRICE EXTERNALITIES 123

to over-produce, and leads to higher levels of production and lower equilibrium values in the best

equilibrium.

Finally, in the following proposition we formalize our numerical illustration from Section 2.3.3 that

the welfare gains from group punishments are increasing in the parameter ρ. For a given set of

parameters, let ∆U denote the change in the value of the best equilibrium in our model relative to

the value of the best equilibrium in the model where group punishments are not allowed, i.e.

∆U ≡u (q)− u

(qA)

u (qA). (B.11)

Proposition 14. Fix ρ ∈ (0, 1). For n sufficiently large, there exists a δ ∈ (0, 1) and ρ > 0 such that for all

ρ′ ∈ (ρ, ρ), d∆U (ρ′) /dρ′ > 0.

We give here a sketch of our argument, and leave a formal proof to Appendix B.2.2. For a fixed level

of the substitutability parameter ρ, we know that our model achieves the first-best level of output

qm at a lower level of the discount factor than the model where taxes are not allowed. This happens

because, as showed in Proposition 8, the threat of taxes always weakly enlarges the equilibrium

set, and strictly enlarges the equilibrium set when producers are sufficiently patient. We denote by

δA∗(ρ) the threshold level of the discount factor at which the model where taxes are not allowed

first achieves qm as the most collusive level of output, and by δ∗(ρ) the level of the discount factor

at which our model first achieves qm as the most collusive level of output. Since δ∗(ρ) < δA∗(ρ), we

can always find a discount factor δ0 such that δ∗(ρ) < δ0 < δA∗(ρ). At δ0 the model where taxes

are allowed achieves qm as the most collusive level of output, while the model where taxes are not

allowed achieves a higher level of output (a lower value) than qm. In the final step of the proof we

argue that by continuity at this δ0, if ρ increases by a sufficiently small amount to some ρ′ > ρ, the

model where taxes are allowed still achieves qm as the most collusive level of output. At δ0, on the

other hand, the most collusive level of output under ρ′ is strictly greater than the most collusive level

of output under ρ in the model where taxes are not allowed (from Lemma 13). Therefore the increase

in output (and decrease in value) relative to qm (the most collusive level of output at δ0, in the model

where taxes are allowed) increases when ρ increases to ρ′. Using the same argument, we prove that

for all ρ′ ∈ (ρ, ρ), d∆U (ρ′) /dρ′ > 0.


Figure B1

Comparative Statics: Marginal Costs of Production and Team Welfare

Percentage increase in welfare in best equilibrium from group punishments for various marginal costs of pro-duction c for a fixed discount factor (δ = 0.16).

Goods Substitutability (ρ)0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

% W

elfa

re C

hang

e

0.04

0.06

0.08

0.1

0.12

0.14

0.16

c = 0.1c = 0.5c = 0.8c = 1

Different parametrizations of the model suggest that the results of Proposition 14 hold for a wide

range of the model’s key parameters. As an example, Figure B1 shows the percentage increase in

welfare in the best equilibrium associated with group punishments for various values of the degree

of substitutability ρ and the marginal cost of production, c. In this figure, we hold the discount factor

fixed at a value of δ = 0.16. This figure clearly shows that an increase in the degree of substitutability

strictly raises the welfare gains associated with group punishments and that these welfare gains are

not particularly sensitive to the marginal costs of production.

B.2 Definitions and Proofs

B.2.1 Definitions and Proofs from Sections 2.2 and 2.3

Repeated Game Definitions

Definition 1. For any history hwt ∈ Hw the continuation game is the infinitely-repeated game that be-

gins in period t, following history hwt. For any strategy profile σ =({σi}n

i=1 , σw), agent i’s continuation

B.2. DEFINITIONS AND PROOFS 125

strategy induced by hwt is given by σi(hwthws) for all hws ∈ Hw, where hwthws is the concatenation of his-

tory hwt followed by history hws. Similarly, the Principal continuation strategy induced by hwt is given by

σw((

hwthws) , x(σ1(hwthws) , σ2

(hwthws) , . . . , σn

(hwthws))) for all hws ∈ Hw.

Definition 2. A Perfect-Public Equilibrium is σ =({σi}n

i=1 , σw)

such that, for all histories hwt ∈ Hw,

Uti(hwt, σ

)≥ Ut

i(hwt, (σi, σ−i, σw)

)(B.12)

for all i, σi, and

Utw(hwt, σ

)≥ Ut

w(hwt,

({σi}n

i=1 , σw))

(B.13)

for all σw.

Definition 3. A one-shot deviation for agent i from strategy σi is a strategy σi 6= σi such that there exists a

unique history hwt ∈ Hw such that for all hws 6= hwt,

σi (hws) = σi (hws) . (B.14)

Similarly, a one-shot deviation for the Principal from strategy σw is a strategy σw 6= σw such that for all

hwt ∈ Hw there exists a level of the total outcome xt such that for all xt 6= xt,

σw(hwt, xt

)= σw

(hwt, xt

). (B.15)

Definition 4. A one-shot deviation σi from the agent strategy σi is profitable if at history hwt for which

σi(hwt) 6= σi

(hwt),

Uti(hwt, (σi, σ−i, σw)

)> Ut

i(hwt, σ

). (B.16)

A one-shot deviation σw from the Principal strategy σw is profitable if for all hwt ∈ Hw, at the outcome level

for which σw(hwt, xt

)6= σw

(hwt, xt

),

Utw(hwt,

({σi}n

i=1 , σw))

> Utw(hwt, σ

). (B.17)


Proof of Proposition 3

If a profile is perfect-public, clearly there are no profitable one-shot deviations. Now suppose that the

profile σ is not perfect-public. We want to show that there must be a profitable one-shot deviation.

Since σ is not perfect-public, there exists a history hwt, an agent i and a strategy σi (the proof for the

Principal follows the same steps) such that

Uti(hwt, σ

)< Ut


). (B.18)

Let ε = Uit(hwt, (σi, σ−i, σw)

)−Ui

t(hwt, σ

). Let m = mini,q,τ ui (q, τ) and M = maxi,q,τ ui (q, τ), with T

large enough that δT (M−m) < ε/2.B.1. Finally, for any agent i and history hws ∈ Hw, let

usi((

hwthws) , σ)

= ui

({σi(hwthws)}n

i=1 , σw((

hwthws) , x(hwthws))) , (B.19)

where x(hwthws) is short-hand notation for x

(σ1(hwthws) , σ2

(hwthws) , . . . , σn

(hwthws)), and denote

by hws the period-s history induced by (σi, σ−i, σw). Then,

(1− δ)

[T−1

∑s=t

δsusi((

hwthws) , σ)

+∞

∑s=T

δsusi((

hwthws) , σ)]

= (1− δ)

[T−1

∑s=0

δsusi((

hwthws) , (σi, σ−i, σw))

+∞

∑s=T

δsusi((

hwthws) , (σi, σ−i, σw))]− ε, (B.20)

so that

(1− δ)T−1

∑s=t

δsusi((

hwthws) , σ)

< (1− δ)T−1

∑s=0

δsusi((

hwthws) , (σi, σ−i, σw))− ε

2. (B.21)

Then the strategy σi such that

σi (hws) =

σi (hws) if s < T,

σi (hws) if s ≥ T,(B.22)

B.1Note that ui (·) is potentially unbounded below. Here we impose that m is an arbitrarily large negative number.


is a profitable deviation from σi(hwt). Now let hw(T−1) denote the period T − 1 history induced by

(σi, σ−i, σw). There are two possibilities. First, suppose

UT−1i

((hwthw(T−1)

), σ)

< UT−1i

((hwthw(T−1)

), (σi, σ−i, σw)

). (B.23)

Then, since σi agrees with σi in period T and after T, we have a profitable one-shot deviation after

history hwthw(T−1). Alternatively, suppose

UT−1i

((hwthw(T−1)

), σ)≥ UT−1

i

((hwthw(T−1)

), (σi, σ−i, σw)

), (B.24)

and construct the strategy

σi (hws) =

σi (hws) if s < T − 1,

σi (hws) if s ≥ T − 1.(B.25)

Since

UT−2i

((hwthw(T−2)

), (σi, σ−i, σw)

)= (1− δ) uT−2

i

((hwthw(T−2)

), (σi, σ−i, σw)

)+ δUT−1

i

((hwthw(T−1)

), (σi, σ−i, σw)

)(B.26)

≤ (1− δ) uT−2i

((hwthw(T−2)

), (σi, σ−i, σw)

)+ δUT−1

i

((hwthw(T−1)

), σ)

(B.27)

= UT−2i

((hwthw(T−2)

), (σi, σ−i, σw)

), (B.28)

then

Uti(hwt, (σi, σ−i, σw)

)≤ Ut


), (B.29)

and σi is a profitable deviation at hwt that only differs from σi in the first T − 1 periods. Proceeding

in this way, we find a profitable one-shot deviation.



We need only prove that for each v ∈ [v, v], there exists a perfect-public equilibrium strategy which

attains the value v. To construct such strategy, we start from the set of perfect-public equilibrium

strategies of the game where the Principal is not allowed to impose group punishments,[vA, vA]. We

know from Abreu (1986) that any equilibrium value v0 such that v0 ∈[vA, vA] can be achieved with

a perfect-public equilibrium strategy σ0. Under σ0, the Principal never imposes group punishments

and agents exert effort a0 such that u(a0) = v0 on path, and punish deviations by both Principal

and agents by reversion to the worst (carrot-and-stick) perfect-public equilibrium with value vA.

Therefore, we focus on characterizing the equilibrium strategies for the cases in which[vA, vA] ⊂

[v, v].

Consider a new strategy σ1. Define by aA the carrot output in the model where group punishments

are not allowed. Under σ1, for some ε1 > 0 agents choose a1 = aA + ε1 as long as the aggregate

outcome x1 is such that x1 = x(a1), and the Principal never imposes punishments. Suppose that

an agent deviates to some a′, such that the observed aggregate outcome is x1 = x(a′, a1). In this

case, the Principal imposes an arbitrarily small punishment τ1 (x1) > 0 such that the punishment is

feasible. That is, such that v1 (a′, a1, τ1 (x1)) ∈ [v, v], where

v1(

a′, a1, τ1(

x1))

≡ 1− δ

δ

1n

[w(

a′, a1, 0)− w

(a′, a1, τ1

(x1))]

. (B.30)

If an agent deviates and the Principal implements the prescribed punishment, then agents follow the

strategy σ1 (v1 (a′, a1, τ1 (x1))). Therefore, the continuation value promised to agents when one of

the agents deviates and the Principal imposes τ1 (x1) can be achieved with a perfect-public equili-

brium strategy. Conversely, deviations by agents followed by deviations by the Principal are punis-

hed by the worst perfect-public equilibrium strategy σ1 (vA). Clearly, this strategy is a perfect-public

equilibrium. Moreover, it achieves a value u(a1) ≡ v1 > vA.

Next, note that reversion to the perfect-public equilibrium v1 > vA allows to construct a new carrot-

and-stick strategy in which agents contribute an effort level a1 < aA for one period and then revert

to v1, with deviations from the prescription causing the prescription to be repeated. Moreover, note


that this new carrot-and-stick strategy has value v1 < vA. Hence, for any value v1 ∈[v1, v1], we can

find a perfect-public equilibrium strategy σ1 such that u(σ1) = v1.

Now take some k ≥ 2 and set[vk, vk

]such that

[v1, v1] ⊂ [

vk, vk]⊂ [v, v], and assume that for

any vk ∈[vk, vk

]we can construct a perfect-public equilibrium strategy σk such that u

(σk)

= vk.

Denote by ak the effort level with value vk, and construct a new strategy σk+1. Under σk+1, for some

εk+1 > 0 agents produce ak+1 = ak + εk+1 as long as the observed aggregate outcome xk+1 is such that

xk+1 = x(

ak+1)

, and the Principal never imposes punishments. Suppose that an agent deviates to

some a′, such that the observed aggregate outcome is xk+1 = x(

a′, ak+1)

. In this case, the Principal

imposes a punishment τk+1(

xk+1)

> 0 such that the punishment is feasible. That is, such that

vk+1(

a′, ak+1, τk+1(

xk+1))∈ [v, v], where

vk+1(

a′, ak+1, τk+1(

xk+1))

≡ 1− δ

δ

1n

[w(

a′, ak+1, 0)− w

(a′, ak+1, τk+1

(xk+1

))]. (B.31)

Note that since vk > v1, the range of punishments that can be sustained is larger than[0, supx1 τ1 (x1)].

If an agent deviates and the Principal implements the prescribed tax, then agents follow the stra-

tegy σk+1(

vk+1(

a′, ak+1, τk+1(

xk+1)))

. Therefore, the continuation value promised to agents when

one of the agents deviates and the Principal imposes τk+1(

xk+1)

can be achieved with a perfect-

public equilibrium strategy. Conversely, deviations by agents followed by deviations by the Princi-

pal are punished by the worst perfect-public equilibrium strategy σk+1(

vk)

. Clearly, this strategy

is a perfect-public equilibrium. Moreover, it achieves a value u(

ak+1)≡ vk+1 > vk. Next, note

that reversion to the perfect-public equilibrium vk+1 > vk allows to construct a new carrot-and-stick

strategy in which agents exert an effort level ak+1 > ak for one period and then revert to vk+1, with

deviations from the prescription causing the prescription to be repeated. Moreover, note that this

new carrot-and-stick strategy has value vk+1 < vk. Hence, for any value vk+1 ∈[vk+1, vk+1

], we can

find a perfect-public equilibrium strategy σk+1 such that u(

σk+1)

= vk+1. The proof is completed by

induction.



Suppose σ ((a, a) , (0, 0)) is an optimal carrot-and-stick punishment. Recalling from Proposition 5

that a ≤ aN , the requirement that producers do not deviate from the stick and carrot outputs a and a

are, respectively:

(1− δ) u (a, 0) + δu (a, 0) ≥ (1− δ) g (a, 0) + δ (1− δ) u (a, 0) + δ2u (a, 0) , (B.32)

u (a, 0) ≥ (1− δ) g (a, τ (·)) + δ (1− δ) u (a, 0) + δ2u (a, 0) . (B.33)

Rearranging these inequalities, we get

g (a, 0) ≤ (1− δ) u (a, 0) + δu (a, 0) = v, (B.34)

g (a, τ (·)) ≤ u (a, 0) + δ (u (a, 0)− u (a, 0)) . (B.35)

If (B.34) holds strictly, we can decrease a and hence reduce u (a, 0) while preserving (B.35). But

this yields a lower punishment value than the infimum v, a contradiction. Hence (B.34) holds with

equality. Now suppose that if a < a∗, (B.35) holds as a strict inequality. Then we can simultaneously

decrease a by a small amount (therefore not violating (B.35)) and increase a to preserve (B.34). But

then since g (a, 0) is increasing in a and (B.34), we also found a lower punishment value than the

infimum, again a contradiction.

Proof of Lemma 10

First, note that

g (q, τ (·)) ≥ maxq′

g(q′, q, τ

(q′ + (n− 1) q

))(B.36)

≥ g(

1− (n− 1) q− c2

, q, τ

(1− (n− 1) q− c

2+ (n− 1) q

)). (B.37)


Moreover, note that

∂g (q′, q, τ)

∂τ= −q′ +

1n(q′ + (n− 1) q

)(B.38)

=n− 1

n(q− q′

), (B.39)

so that ∂g (q, q′, τ) /∂τ ≥ 0 if and only if q′ ≤ q. Finally, for q ≥ qN if we choose the deviation

q′ =1− (n− 1) q− c

2, (B.40)

then it must be that q′ ≤ q, since

1− (n− 1) q− c2

≤ q ⇐⇒ qN ≤ q. (B.41)

Hence, for q ≥ qN ,

g (q, τ (·)) ≥ g(

1− (n− 1) q− c2

, q, τ

(1− (n− 1) q− c

2+ (n− 1) q

))(B.42)

≥ g(

1− (n− 1) q− c2

, q, 0)

(B.43)

= g (q, 0) . (B.44)

B.2.2 Proofs from Appendix B.1

Proof of Lemma 12

The proof is a straightforward extension of the proof found in Appendix B.2.1. In absence of a closed-

form for the optimal deviation for the model where taxes are not allowed, the only additional step

required to complete the proof is to show that for q ≥ qN if we choose the deviation

q′ = q (q) , (B.45)

then q′ ≤ q. We prove this by showing that q (q) is a smooth function that only intersects the 45

degree line at zero and qN , and that for some q > qN , q (q) < q. First, note that q (0) = 0, and that

by definition of Nash equilibrium for q > 0, q (q) = q if and only if q = qN . Moreover, note that


q (q) is smooth, since the problem is smooth and q (q) is the implicit function that generates from the

first order conditions determining the most profitable deviation from q. Finally, note that for some

q > qN , q (q) < q. To show this, consider any q > q0, where q0 is the minimum q > 0 such that

q (q) = 0 if and only if g (q, τ = 0) = 0. This level of q exists (as q goes to infinity, the price is driven to

zero and the most profitable deviation is not to produce and avoid the associated cost) and we can

always find it large enough such that q > qN .

Proof of Lemma 13

Since in what follows we focus on a model where taxes are not allowed, for notational convenience

we drop functional dependencies on taxes (e.g. we denote u(q, 0) by u(q)). We similarly drop the

superscript “A” which we use to compare the model where taxes are allowed to the model where

taxes are not allowed. To show that for sufficiently large n, dq/dρ > 0, we analyze the two equations

that characterize the carrot and the stick output in the model where taxes are not allowed, i.e.

g (q (ρ) ; ρ) =α

n− (1− δ)cq (ρ)− δcq (ρ) , (B.46)

g (q (ρ) ; ρ) =α

n− (1 + δ)cq(ρ) + δcq (ρ) . (B.47)

Totally differentiating these two expressions, we obtain

gq (q (ρ) ; ρ)dq(ρ)

dρ+ gρ (q (ρ) ; ρ) = −(1− δ)c

dq(ρ)dρ− δc

dq (ρ)dρ

(B.48)

gq (q (ρ) ; ρ)dq(ρ)

dρ+ gρ (q (ρ) ; ρ) = −(1 + δ)c

dq (ρ)dρ

+ δcdq (ρ)

dρ(B.49)

We solve for dq/dρ from the first equation and substitute into the second to obtain a form for dq/dρ.

We have

[gq (q (ρ) ; ρ) + (1− δ) c

] dq(ρ)dρ

= −gρ (q (ρ) ; ρ)− δcdq (ρ)

dρ, (B.50)

so that

[gq (q (ρ) ; ρ) + (1 + δ)c

] dq(ρ)dρ

= −gρ (q (ρ) ; ρ) + δc

−gρ (q (ρ) ; ρ)− δc dq(ρ)dρ

gq (q (ρ) ; ρ) + (1− δ) c

. (B.51)


To be able to determine the sign of dq/dρ, we determine the sign of the derivatives gq (q; ρ) and

gq (q; ρ). First, for any q we denote the most profitable deviation from q as a function of q and ρ as

q∗ (q, ρ). From the optimality conditions, we know that any q∗ (q, ρ) satisfies

αρ (n− 1) qρ (q∗)−ρ−1[1 + (n− 1) qρ (q∗)−ρ

]2 = c. (B.52)

Next, note that the payoff from the best response satisfies

gq (q; ρ) =ddq

[α

1 + (n− 1) qρq∗ (q, ρ)−ρ − q∗ (q, ρ) c

](B.53)

=−α[

1 + (n− 1) qρq∗ (q, ρ)−ρ]2

[(n− 1) ρqρ−1q∗ (q, ρ)−ρ

− (n− 1) ρqρq∗ (q, ρ)−ρ−1 q∗q (q, ρ)]− cq∗q (q, ρ) (B.54)

=−αρ (n− 1) qρ−1q∗ (q, ρ)−ρ[

1 + (n− 1) qρq∗ (q, ρ)−ρ]2 +

α (n− 1) ρqρq∗ (q, ρ)−ρ−1[1 + (n− 1) qρq∗ (q, ρ)−ρ

]2 − c

q∗q (q, ρ) (B.55)

=−αρ (n− 1) qρ (q∗)−ρ

q[1 + (n− 1) qρ (q∗)−ρ

]2 , (B.56)

where the last equality follows from optimality of q∗. Note also that using optimality of q∗, we may

write gq (q; ρ) as

gq (q; ρ) =−αρ (n− 1) qρ (q∗)−ρ

q[1 + (n− 1) qρ (q∗)−ρ

]2 = − cq∗ (q, ρ)

q. (B.57)

Since if q < qN then q∗(q, ρ) ≥ q and if q ≥ qN then q∗(q, ρ) ≤ qN , this implies

gq (q; ρ) ≤ −c if q < qN , (B.58)

gq (q; ρ) ≥ −c if q ≥ qN . (B.59)


Similarly, note that

gρ (q; ρ) =d

dρ

[α

1 + (n− 1) qρq∗ (q, ρ)−ρ − q∗ (q, ρ) c

](B.60)

=−α (n− 1) q∗ (q, ρ)−ρ qρ[1 + (n− 1) qρq∗ (q, ρ)−ρ

]2 [log q− log q∗(q, ρ)] , (B.61)

so that we can write

gρ (q; ρ) = − cρ

q∗ (q, ρ) [log q− log q∗(q, ρ)] . (B.62)

We then have

gρ (q; ρ) ≥ 0 if q < qN , (B.63)

gρ (q; ρ) ≤ 0 if q ≥ qN . (B.64)

Next, substituting (B.57) and (B.62) into (B.51), we obtain

dq(ρ)dρ

[gq (q (ρ) ; ρ) + (1 + δ)c +

δ2c2

gq (q (ρ) ; ρ) + (1− δ) c

]= −gρ (q (ρ) ; ρ)

−δcgρ (q (ρ) ; ρ)

gq (q (ρ) ; ρ) + (1− δ) c(B.65)

Simplifying and using short-hand notation, we have

qρ

− q∗

q+ (1 + δ) +

δ2

− q∗

q + (1− δ)

=1ρ

q∗ log(

qq∗

)+

δ 1ρ q∗ log

(qq∗

)− q∗

q + (1− δ)(B.66)

qρ

1− q∗

q+

δ[1− q∗

q

]1− q∗

q − δ

=1ρ

q∗ log(

qq∗

)+

δ 1ρ q∗ log

(qq∗

)1− q∗

q − δ(B.67)

qρ

[q− q∗

q+

δ [q− q∗](1− δ)q− q∗

]=

1ρ

q∗ log(

qq∗

)+

δ 1ρ qq∗ log

(qq∗

)(1− δ)q− q∗

. (B.68)

Since q ≤ q∗ and q ≥ q∗, if

(1− δ)q− q∗ ≤ 0, (B.69)


then each term in brackets on the left-hand side and each term on the right-hand side of (B.68) are

negative. This implies qρ ≥ 0. Hence, (1− δ)q− q∗ ≤ 0 is a sufficient condition for qρ to be positive.

To show this, we use the expression for g(q, ρ) and g(q, ρ) in (B.46) and (B.47):

α

1 + (n− 1)(

qq∗

)ρ − cq∗ =α

n− (1− δ)cq− δcq, (B.70)

α

1 + (n− 1)(

qq∗

)ρ − cq∗ =α

n− (1 + δ)cq + δcq. (B.71)

Equation (B.71) implies

(1 + δ)cq− cq∗ =α

n− α

1 + (n− 1)(

qq∗

)ρ + δcq (B.72)

≤ δcq, (B.73)

which substituted into (B.70) yields

(1− δ)cq− cq∗ =α

n− α

1 + (n− 1)(

qq∗

)ρ − δcq (B.74)

= (1 + δ)cq− cq∗ +α

1 + (n− 1)(

qq∗

)ρ −α

1 + (n− 1)(

qq∗

)ρ − δc (q + q) (B.75)

≤ δcq +α

1 + (n− 1)(

qq∗

)ρ −α

1 + (n− 1)(

qq∗

)ρ − δc (q + q) . (B.76)

Then, we have

(1− δ)cq− cq∗ ≤ −δcq +α

1 + (n− 1)(

qq∗

)ρ −α

1 + (n− 1)(

qq∗

)ρ . (B.77)

For n sufficiently large, q∗ converges to q and q∗ converges to q. Hence, for n sufficiently large the

right-hand side is less than or equal to zero and the needed condition is verified.



Fix ρ ∈ (0, 1). We know that there exist a unique δA∗ (ρ) in the model where taxes are not allowed

such that qA (ρ) = qm. This δA∗ (ρ) simultaneously solves

g (qm, 0) =(

1 + δA∗ (ρ))

u (qm)− δA∗ (ρ) u(

qA (ρ))

, (B.78)

g(

qA (ρ) , 0)

=(

1− δA∗ (ρ))

u(

qA (ρ))

+ δA∗ (ρ) u (qm) , (B.79)

and represents the threshold level of the discount factor for which the model where taxes are not

allowed achieves the first-best level of output qm. Similarly, for the same ρ we know that there exists

a unique δ∗ (ρ) in the model where taxes are allowed such that q (ρ) = qm, which simultaneously

solves

g (qm, τ (·)) = (1 + δ∗ (ρ)) u (qm)− δ∗ (ρ) u (q (ρ)) , (B.80)

g (q (ρ) , 0) = (1− δ∗ (ρ)) u (q (ρ)) + δ∗ (ρ) u (qm) . (B.81)

Next, note that since i) for any level of the discount factor we have[vA; vA] ⊆ [v; v], and ii) for

qA > qm if q is sustained by a positive tax threat (for some q′ 6= q, τ (q′ + (n− 1) q) > 0) then

qA > q ≥ qm, then δ∗ (ρ) < δA∗ (ρ) (i.e. the model where taxes are allowed achieves the first best

level of output qm at a lower value of the discount factor than the model where taxes are not allowed).

Next, let δ0 be such that δ∗ (ρ) < δ0 < δA∗ (ρ). Note that at δ0, q (ρ) = qm and qA (ρ) > qm. Now let

ρ′ > ρ, and let δ∗ (ρ′) in the model where taxes are allowed be such that q (ρ′) = qm, which solves

g (qm, τ (·)) =(1 + δ∗

(ρ′))

u (qm)− δ∗ (ρ) u(q(ρ′))

(B.82)

g(q(ρ′)

, 0)

=(1− δ∗

(ρ′))

u(q(ρ′))

+ δ∗ (ρ) u (qm) . (B.83)

By continuity we know that we can always choose ρ′ small enough such that δ∗ (ρ′) < δ0. Therefore,

in the model where taxes are allowed q (ρ′) = q (ρ) = qm. Moreover, since from Lemma 13 we know

that for n sufficiently large dqA/dρ > 0, then qA (ρ′) > qA (ρ). Hence, at δ0

u (q (ρ′))− u(qA (ρ′)

)u (qA (ρ′))

>u (q (ρ))− u

(qA (ρ)

)u (qA (ρ))

. (B.84)

B.3. COMPUTATIONAL ALGORITHM 137

Finally, following the same argument we have that for all ρ′ ∈ (ρ, ρ′), d∆U (ρ′) /dρ′ > 0.

B.3 Computational Algorithm

In this Appendix, we describe the computational algorithm for our numerical results in Section 2.3.

Define q ≡ arg maxq′ g (q′, q, τ (q′ + (n− 1) q)). For each level of the discount factor δ, we aim to find

q, q, q and τ that solve the following system of equations:

g (q, 0) = (1− δ) u (q, 0) + δµ (q, 0) , (B.85)

g (q, τ (·)) ≤ u (q, 0) + δ (u (q, 0)− u (q, 0)) , (B.86)

u (q, 0) ≥ 1− δ

δ

1n[w (q + (n− 1) q, 0)− w (q + (n− 1) q, τ (q + (n− 1) q))]

+g (q, 0) . (B.87)

From Proposition 7, Equation (B.86) holds with equality only when q > qm and is slack when q = qm.

The algorithm works as follows:

1. For each level of the discount factor δ, we know τ ∈[0, 1− (n− 1) qN − c

]. Start with τ =

1− (n− 1) qN − c.

(a) Check if qm can be supported:

i. Set q = qm. Solve (B.85) for q.

ii. Obtain q = arg maxq′∈[qm ,qN] g (q′, q, τ). We do this by searching for q over a fine grid

for q′. Evaluate g (q, τ).

iii. Check if the resulting values for q and q satisfy (B.86) (with inequality) and (B.87). If

so, the algorithm is finished.

(b) If either (B.86) or (B.87) is not satisfied (qm cannot be supported), jointly solve for q and q.

We do this using a nested bisection algorithm to solve (B.85) and (B.86) with equality (also

solving for q as before).


i. The nested bisection algorithm proceeds as follows. The outer bisection algorithm

searches for q ∈ [q`, qh]. The inner bisection algorithm solves for the corresponding q.

ii. At each iteration of the double bisection algorithm, check whether (B.85)-(B.87) are all

satisfied.

2. If (B.85) and (B.87) are satisfied, we are done. If not decrease τ by a small amount and return

to step 1.

Appendix C


139

140 APPENDIX C. APPENDIX TO CHAPTER 3

C.1 Cointegration Tests

In Table C1, I report two sets of tests for cointegration between real, per-capita advertising expen-

ditures and consumption. In Panel A, I use the Phillips and Ouliaris (1990) procedure to test for a

unit root in the residual of a regression of advertising expenditures on consumption, assuming no

trend in the residuals. Panel A of Table C1 reports the Dickey and Fuller (1979) t-statistic for a unit

root in the residuals using lags from one to four years, and the associated five and ten percent critical

values. The null hypothesis of no cointegrating relationship can never be rejected at any horizon. I

use the procedure in Campbell and Perron (1991) to determine the appropriate number of lags of first

differences in the regression of residuals on lagged residuals and lagged first differences of residuals,

and the results of this procedure suggest that the optimal number of lag is three years. The results of

Panel A provide evidence against cointegration at the optimal lag length.

As a second test, I apply the Johansen (1988, 1991) procedure to estimate the number of cointegrating

relationships between advertising expenditures and consumption, assuming that the cointegrating

relation should be characterized by an unrestricted constant.C.1 The Johansen trace statistic tests

the null hypothesis H0 = r of at most r cointegrating relations in the data against the alternative

hypothesis of p cointegrating relations, where p is the number of variables (two in this case), and the

null hypothesis is rejected at the five percent confidence level if the trace statistics is larger than its

respective critical value. Table C1, Panel B, shows that the test can never reject the null hypothesis of

zero cointegrating relationships between advertising and consumption at any of the lags considered.

Despite the weak evidence about cointegration between advertising expenditures and consumption,

in Table C2 I re-estimate the consumption growth predictive regressions of Table 3.2, Panel A, using

a vector-error-correction model (VECM). The estimated VECM corrects the predictive regressions

with a cointegrating residual capturing deviations of either consumption or advertising from their

long-run common trend. The results show that correcting for this cointegrating residual decreases

the predictive power of advertising at a two-year horizon, but leaves leaves the predictive power of

advertising unchanged at a one-year horizon.

C.1This assumption is common in modeling macroeconomic variables. See Johansen (1988, 1991) for details.

C.1. COINTEGRATION TESTS 141

Table C1

Philips-Ouliaris and Johansen Tests for Cointegration

In Panel A, the Dickey and Fuller (1979) test statistics is applied to the fitted residuals of a regression of per-capita real advertising expenditures on per-capita real consumption. No trend is assumed in the residuals.The procedure in Campbell and Perron (1991) is used to to determine the number of lags of first differences inthe regression of residuals on lagged residuals and lagged first differences of residuals. In Panel B, I apply theJohansen (1988, 1991) trace statistic assuming that the relation between consumption and advertising expendi-tures in the data is governed by VAR model with unrestrticted constant. The null hypothesis H0 = r of at mostr cointegrating relationships in the data is rejected at the 5% confidence level if the trace statistics is larger thanthe respective critical value.

Panel A: Philips-Ouliaris Test

Dickey-Fuller t-statistic Critical ValuesLag=1 Lag=2 Lag=3 Lag=4 5% 10%

-1.346 -2.190 -2.290 -2.389 -2.926 -2.598

Panel B: Johansen Trace Statistic

Johansen Trace Statistic Critical Value H0 = rLag=1 Lag=2 Lag=3 Lag=4 5% r =

12.591 6.594 4.321 5.978 15.41 04.086 2.426 0.263 0.472 3.76 1


Table C2

Vector-Error-Correction Model for Consumption Growth Predictions, Post-War Period

The Table shows coefficient estimates for cumulative consumption growth (∆ct→t+τ) predictive regressionsusing a Vector-Error-Correction model including lagged advertising growth (∆at−1→t), consumption growth(∆ct−1→t), and their long-run cointegrating residual ε(a, c)t−1 as predictors. The t-statistics in parentheses arecomputed using Hansen and Hodrick (1980) standard errors. R2


∆ct→t+1 ∆ct→t+2 ∆ct→t+3 ∆ct→t+4

∆at−1→t 0.112 0.162 0.151 0.111(2.06) (1.56) (1.01) (0.62)

∆ct−1→t 0.027 -0.160 -0.274 -0.309(0.17) (-0.53) (-0.65) (-0.60)

ε(a, c)t−1 -0.012 -0.032 -0.044 -0.054(-0.86) (-0.98) (-0.87) (-0.81)

R2adj 0.124 0.080 0.031 0.007F 3.545 1.669 0.756 0.446

C.2 Advertising Expenditures and Long-Run Risk

In this Section, I claim that the time series properties of aggregate advertising growth make this

variable a quantitatively different source of consumption dynamics than the aggregate consumption

growth risk in the Bansal and Yaron (2004) long-run risk model. The Bansal and Yaron (2004) long-

run risk model specifies the following process for consumption growth (for consistency with their

model I use ∆ct+1 to denote the consumption growth rate ∆ct→t+1):

∆ct+1 = κ + xt + σηt+1, (C.1)

xt+1 = ρxt + φeσet+1, (C.2)

et+1, ηt+1 ∼ N.i.i.d (0, 1) , (C.3)

where the shocks et+1 and ηt+1 are mutually independent. In their model, xt is a small and persis-

tent predictable component that determines the expected growth rate of consumption and ρ is the

C.2. ADVERTISING EXPENDITURES AND LONG-RUN RISK 143

persistence of this predictable component, calibrated to a monthly ρ = 0.979 (annual ρann = 0.775) to

replicate the annualized volatility and autocorrelation of aggregate consumption growth.

On the other hand, the VAR specification from Panel A of Table 3.5 implies the following relation

between consumption growth, advertising expenditures and their lagged values:

∆ct+1 = αc + γc∆at + uc,t+1, (C.4)

∆at+1 = αa + βa∆ct + γa∆at + ua,t+1, (C.5)

uc,t+1, ua,t+1, ∼ N (0, Σ) , (C.6)

with Σ the variance-covariance matrix of the residuals. For simplicity, I omit the VAR coefficients that

are not statistically significant. The point estimate of the coefficient γc in Equation (C.4) is 0.127, and

its standard deviation is 0.050. The point estimates for the coefficients βa and γa in Equation (C.5)

are 0.679 and -1.147, respectively, and their standard deviations are 0.144 and 0.456, respectively.

The following analysis is to test whether, given these estimates, Equations (C.4) and (C.5) can re-

spectively be re-written as Equations (C.1) and (C.2), that is whether advertising growth captures

the long-run persistent component of consumption growth that generates long-run risk. First, define

∆at ≡ γc∆at, so that (C.4)-(C.5) can be re-written as

∆ct+1 = αc + ∆at + uc,t+1, (C.7)

∆at+1 = γcαa + γcβa∆ct + γc∆at + γcua,t+1 (C.8)

Testing if (C.5) is equivalent to the long-run risk equation (C.2) then means simultaneously testing for

γcαa = γcβa = 0 and γc = ρann = 0.775. Since the point estimate for γc in Table 3.5 is however equal

to 0.127 with a 95 percent confidence interval of [0.029; 0.225], I cannot reject the null hypothesis that

γc 6= ρann. This suggests that advertising growth predicts a component of aggregate consumption

growth not captured by long-run risk.


C.3 Derivation of the Stochastic Discount Factor

The derivative of (3.20) with respect to C0,t is

∂Vt

∂C0,t= (1− β) (1− α) V

1ψ

t u (C0,t; C1,t)1η−

1ψ C− 1

η

0,t . (C.9)

The derivative of (3.20) with respect to C0,t+1 is

∂Vt

∂C0,t+1= V

1ψ

t βEt

[V1−γ

t+1

] 1−1/ψ1−γ −1

V−γt+1

∂Vt+1

∂C0,t+1. (C.10)

Replacing ∂Vt+1/∂C0,t+1 by (C.9) evaluated at t + 1, I get

Mt+1 =∂Vt/∂C0,t+1

∂Vt/∂C0,t(C.11)

= β

(C0,t+1

C0,t

)− 1η(

u (C0,t+1; C1,t+1)

u (C0,t; C1,t)

) 1η−

1ψ

Vt+1

Et

(V1−γ

t+1

) 11−γ

1ψ−γ

. (C.12)

C.4 Computational Algorithm

The state space consists of aggregate endowment and customer capital, (Yt, Nt), and the objective

is to solve for optimal advertising AD∗t = AD (Yt, Nt) and the multiplier on its non-negativity con-

straint µn∗t = µn (Yt, Nt) from the functional Euler equation

χ

λt

ADt

Nt− µn (Yt, Nt) = Et Mt+1

[Pt+1 + (1− ϕ)

(χ


)], (C.13)

where both λt and Pt are functions of AD (Yt, Nt). The algorithm works as follows. I start by approx-

imating the left-hand side of (C.13) with a function

Et ≡ E (Yt, Nt) = Et Mt+1

[Pt+1 + (1− ϕ)

(χ


)]. (C.14)

Since the function Et is defined over the grid (Yt, Nt), I can similarly define

E (Yt, Nt) ≡1χ(NtE (Yt, Nt)) . (C.15)

C.4. COMPUTATIONAL ALGORITHM 145

Finally, since λ =(1 + ADϑ

)−1/ϑ, I calculate a guess ÃD (Yt, Nt) for the policy function AD (Yt, Nt)

by solving

ÃD (Yt, Nt)(

1 + ÃD (Yt, Nt)ϑ) 1

ϑ = E (Yt, Nt) , (C.16)

so that solving function for effort is:C.2

ÃD (Yt, Nt) = 2−1ϑ

(√4E (Yt, Nt)

ϑ + 1− 1) 1

ϑ

. (C.17)

If AD (Yt, Nt) > 0, then the non-negativity constraint on effort is not binding, AD (Yt, Nt) = ÃD (Yt, Nt)

and µn (Yt, Nt) = 0. If instead ÃD (Yt, Nt) ≤ 0, then AD (Yt, Nt) = 0 and µn (Yt, Nt) = −E (Yt, Nt) .

C.2The smaller root of Equation (C.16),

E (Yt , Nt) = 2−1ϑ

(−√

4E (Yt , Nt)ϑ + 1− 1

) 1ϑ

,

is always negative.

Bibliography

ABREU, D. (1986): “Extremal equilibria of oligopolistic supergames,” Journal of Economic Theory, 39,

191–225. iii, 39, 40, 44, 48, 54, 55, 57, 65, 128

ACEMOGLU, D. AND A. WOLITZKY (2015): “Sustaining Cooperation: Community Enforcement vs.

Specialized Enforcement,” Tech. rep., National Bureau of Economic Research. 42

ADRIAN, T., E. FRIEDMAN, AND T. MUIR (2015): “The cost of capital of the financial sector,” CEPR

Discussion Paper No. DP11031. 34, 117

AGARWAL, S., D. LUCCA, A. SERU, AND F. TREBBI (2014): “Inconsistent regulators: Evidence from

banking,” The Quarterly Journal of Economics, 129, 889–938. 5

AI, H., M. M. CROCE, AND K. LI (2013): “Toward a quantitative general equilibrium asset pricing

model with intangible capital,” Review of Financial Studies, 26, 491–530. 70

ALCHIAN, A. A. AND H. DEMSETZ (1972): “Production, information costs, and economic organiza-

tion,” The American Economic Review, 62, 777–795. 41

ALDASHEV, G. AND G. ZANARONE (2017): “Endogenous enforcement institutions,” Journal of Deve-

lopment Economics, 128, 49–64. 42

AMIHUD, Y. (2002): “Illiquidity and stock returns: cross-section and time-series effects,” Journal of

Financial Markets, 5, 31–56. 34, 117

BAGWELL, K. (2007): “The economic analysis of advertising,” Handbook of industrial organization, 3,

1701–1844. 68

147

148 BIBLIOGRAPHY

BANSAL, R. AND A. YARON (2004): “Risks for the long run: A potential resolution of asset pricing

puzzles,” The Journal of Finance, 59, 1481–1509. 83, 92, 142

BARTH, J. R., C. LIN, Y. MA, J. SEADE, AND F. M. SONG (2013): “Do bank regulation, supervision

and monitoring enhance or impede bank efficiency?” Journal of Banking & Finance, 37, 2879–2892.

5

BELO, F., X. LIN, AND S. BAZDRESCH (2014a): “Labor Hiring, Investment, and Stock Return Predic-

tability in the Cross Section,” Journal of Political Economy, 122, 129–177. 70

BELO, F., X. LIN, AND M. A. VITORINO (2014b): “Brand capital and firm value,” Review of Economic

Dynamics, 17, 150–169. 70

BERK, J. B., R. C. GREEN, AND V. NAIK (1999): “Optimal investment, growth options, and security

returns,” The Journal of Finance, 54, 1553–1607. 70

BERTRAND, M. AND S. MULLAINATHAN (2003): “Enjoying the quiet life? Corporate governance and

managerial preferences,” Journal of Political Economy, 111, 1043–1075. 5

BIANCHI, J. (2009): “Overborrowing and systemic externalities in the business cycle,” Federal Reserve

Bank of Atlanta Working Paper Series. 92

BRODA, C. AND D. E. WEINSTEIN (2010): “Product Creation and Destruction: Evidence and Price

Implications,” The American Economic Review, 691–723. 91

BRONNENBERG, B. J., J.-P. H. DUBE, AND M. GENTZKOW (2012): “The Evolution of Brand Prefe-

rences: Evidence from Consumer Migration,” American Economic Review, 102, 2472–2508. 91

BUCHAK, G., G. MATVOS, T. PISKORSKI, AND A. SERU (2017): “Fintech, Regulatory Arbitrage, and

the Rise of Shadow Banks,” Working Paper 23288, National Bureau of Economic Research. 6

CAMPBELL, J. Y. AND J. H. COCHRANE (2000): “Explaining the Poor Performance of Consumption-

based Asset Pricing Models,” The Journal of Finance, 55, 2863–2878. 70

BIBLIOGRAPHY 149

CAMPBELL, J. Y. AND P. PERRON (1991): “Pitfalls and Opportunities: What Macroeconomists Should

Know About Unit Roots,” NBER Technical Working Papers 0100, National Bureau of Economic

Research, Inc. 140, 141

CAMPBELL, J. Y. AND S. B. THOMPSON (2008): “Predicting excess stock returns out of sample: Can

anything beat the historical average?” Review of Financial Studies, 21, 1509–1531. 83, 85

CHE, Y.-K. AND S.-W. YOO (2001): “Optimal Incentives for Teams,” The American Economic Review,

91, 525–541. 42

CHENG, C. (2016): “Moral Hazard in Teams with Subjective Evaluations,” Tech. rep., Northwestern

University. 42

CLARK, T. E. AND K. D. WEST (2007): “Approximately normal tests for equal predictive accuracy in

nested models,” Journal of Econometrics, 138, 291–311. 83, 85

COCHRANE, J. H. (1991): “Production-based asset pricing and the link between stock returns and

economic fluctuations,” The Journal of Finance, 46, 209–237. 70, 88

——— (1996): “A Cross-Sectional Test of an Investment-Based Asset Pricing Model,” Journal of Poli-

tical Economy, 572–621. 70

COLES, J. L., M. L. LEMMON, AND J. F. MESCHKE (2012): “Structural models and endogeneity in

corporate finance: The link between managerial ownership and corporate performance,” Journal

of Financial Economics, 103, 149–168. 5

CORRADO, C. J. (2011): “Event studies: A methodology review,” Accounting & Finance, 51, 207–234.

102

CORWIN, S. A. AND P. SCHULTZ (2012): “A simple way to estimate bid-ask spreads from daily high

and low prices,” The Journal of Finance, 67, 719–760. 34, 117

DANG, T. V., G. GORTON, B. HOLMSTROM, AND G. ORDONEZ (2017): “Banks as secret keepers,”

The American Economic Review, 107, 1005–1029. 5

150 BIBLIOGRAPHY

DEN HAAN, W. (2013): “Inventories and the Role of Goods-Market Frictions for Business Cycles,”

Tech. rep., CEPR Discussion Papers. 70

DEN HAAN, W. J., G. RAMEY, AND J. WATSON (2000): “Job Destruction and Propagation of Shocks,”

American Economic Review, 482–498. 85

DICKEY, D. A. AND W. A. FULLER (1979): “Distribution of the estimators for autoregressive time

series with a unit root,” Journal of the American Statistical Association, 74, 427–431. 75, 76, 140, 141

DROZD, L. A. AND J. B. NOSAL (2012): “Understanding international prices: Customers as capital,”

The American Economic Review, 364–395. 70, 85

EISENBACH, T. M., A. F. HAUGHWOUT, B. HIRTLE, A. KOVNER, D. O. LUCCA, AND M. PLOSSER

(2017): “Supervising large, complex financial institutions: What do supervisors do?” Economic

Policy Review, 57–77. 7

EISFELDT, A. L. AND D. PAPANIKOLAOU (2013): “Organization Capital and the Cross-Section of

Expected Returns,” The Journal of Finance, 68, 1365–1406. 70

ELLUL, A. AND V. YERRAMILLI (2013): “Stronger risk controls, lower risk: Evidence from US bank

holding companies,” The Journal of Finance, 68, 1757–1803. 25, 26

EPSTEIN, L. G. AND S. E. ZIN (1989): “Substitution, risk aversion, and the temporal behavior of

consumption and asset returns: A theoretical framework,” Econometrica, 937–969. 89

FALATO, A., D. KADYRZHANOVA, AND U. LEL (2014): “Distracted directors: Does board busyness

hurt shareholder value?” Journal of Financial Economics, 113, 404–426. 5

FAN, J. AND I. GIJBELS (1996): Local polynomial modelling and its applications: monographs on statistics

and applied probability 66, vol. 66, CRC Press. 16, 17

FERREIRA, M. A. AND P. MATOS (2008): “The colors of investors’ money: The role of institutional

investors around the world,” Journal of Financial Economics, 88, 499–533. 5

FERSON, W. E. AND R. W. SCHADT (1996): “Measuring fund strategy and performance in changing

economic conditions,” Journal of Finance, 425–461. 70

BIBLIOGRAPHY 151

FICH, E. M., J. HARFORD, AND A. L. TRAN (2015): “Motivated monitors: The importance of insti-

tutional investors’ portfolio weights,” Journal of Financial Economics, 118, 21–48. 31

FUCHS, W. (2007): “Contracting with repeated moral hazard and private evaluations,” The American

Economic Review, 97, 1432–1448. 42

FUDENBERG, D. AND E. MASKIN (1986): “The Folk Theorem in Repeated Games with Discounting

or with Incomplete Information,” Econometrica, 54, 533–554. 42

FUDENBERG, D. AND J. TIROLE (1995): “A theory of income and dividend smoothing based on

incumbency rents,” Journal of Political Economy, 103, 75–93. 3, 25

GALE, D. AND M. HELLWIG (1985): “Incentive-compatible debt contracts: The one-period problem,”

The Review of Economic Studies, 52, 647–663. 5, 9

GANDHI, P. AND H. LUSTIG (2015): “Size anomalies in US bank stock returns,” The Journal of Finance,

70, 733–768. 3, 33, 115

GOETZ, M. R., L. LAEVEN, AND R. LEVINE (2013): “Identifying the valuation effects and agency

costs of corporate diversification: Evidence from the geographic diversification of US banks,” The

Review of Financial Studies, 26, 1787–1823. 5

——— (2016): “Does the geographic expansion of banks reduce risk?” Journal of Financial Economics,

120, 346–362. 12

GOLDLUCKE, S. AND S. KRANZ (2012): “Infinitely repeated games with public monitoring and mo-

netary transfers,” Journal of Economic Theory, 147, 1191–1221. 41

——— (2013): “Renegotiation-proof relational contracts,” Games and Economic Behavior, 80, 157–178.

41

GORTON, G. AND G. PENNACCHI (1990): “Financial intermediaries and liquidity creation,” The Jour-

nal of Finance, 45, 49–71. 5

GOURIO, F. AND L. RUDANKO (2014): “Customer Capital,” The Review of Economic Studies, 81, 1102–

1136. iii, 68, 70, 86, 91, 97

152 BIBLIOGRAPHY

GOYENKO, R. Y., C. W. HOLDEN, AND C. A. TRZCINKA (2009): “Do liquidity measures measure

liquidity?” Journal of Financial Economics, 92, 153–181. 34

GROSSMAN, S. J. AND O. D. HART (1980): “Takeover bids, the free-rider problem, and the theory of

the corporation,” The Bell Journal of Economics, 42–64. 4, 30

HALL, R. E. (2014): “What the cyclical response of advertising reveals about markups and other

macroeconomic wedges,” Hoover Institution, Stanford University. 70, 71, 72, 73, 74, 76

HANSEN, L. P. AND R. J. HODRICK (1980): “Forward exchange rates as optimal predictors of future

spot rates: An econometric analysis,” The Journal of Political Economy, 829–853. 75, 77, 78, 79, 82, 94,

96, 142

HARRINGTON, J. E. AND A. SKRZYPACZ (2007): “Collusion under monitoring of sales,” The RAND

Journal of Economics, 38, 314–331. 41

——— (2011): “Private monitoring and communication in cartels: Explaining recent collusive practi-

ces,” The American Economic Review, 101, 2425–2449. 41

HART, O. AND B. HOLMSTROM (1986): The Theory of Contracts, Department of Economics, Massa-

chusetts Institute of Technology. 41

HARVEY, C. R. (1988): “The real term structure and consumption growth,” Journal of Financial Econo-

mics, 22, 305–333. 82

HEATHCOTE, J. AND F. PERRI (2002): “Financial autarky and international business cycles,” Journal

of Monetary Economics, 49, 601 – 627. 92

HIMMELBERG, C. P., R. G. HUBBARD, AND D. PALIA (1999): “Understanding the determinants

of managerial ownership and the link between ownership and performance,” Journal of Financial

Economics, 53, 353–384. 5

HIRTLE, B., A. KOVNER, AND M. C. PLOSSER (2016): “The impact of supervision on bank perfor-

mance,” Working paper. 5

BIBLIOGRAPHY 153

HOLDEN, C. W. (2009): “New low-frequency spread measures,” Journal of Financial Markets, 12, 778

– 813. 34, 117

HOLMSTROM, B. (1982): “Moral hazard in teams,” The Bell Journal of Economics, 324–340. 4, 30

HOLMSTROM, B. (1982): “Moral Hazard in Teams,” The Bell Journal of Economics, 13, 324–340. 38, 40,

41, 43

HOU, K. AND T. J. MOSKOWITZ (2005): “Market frictions, price delay, and the cross-section of ex-

pected returns,” The Review of Financial Studies, 18, 981–1020. 34, 117

HUANG, D. (2015): “Gold, Platinum, and Expected Stock Returns,” Working paper. 78

HUIZINGA, H. AND L. LAEVEN (2012): “Bank valuation and accounting discretion during a financial

crisis,” Journal of Financial Economics, 106, 614–634. 28

HUO, Z. AND J.-V. R IOS-RULL (2013): “Paradox of thrift recessions,” Tech. rep., National Bureau of

Economic Research. 92

HURWICZ, L. (2008): “But who will guard the guardians?” The American Economic Review, 98, 577–

585. 42

HUTTON, A. P., A. J. MARCUS, AND H. TEHRANIAN (2009): “Opaque financial reports, R2, and

crash risk,” Journal of Financial Economics, 94, 67–86. 3, 33

ILIEV, P. (2010): “The Effect of SOX Section 404: Costs, Earnings Quality, and Stock Prices,” The

Journal of Finance, 65, 1163–1196. 25, 109

JAGANNATHAN, R. AND Z. WANG (1996): “The conditional CAPM and the cross-section of expected

returns,” Journal of Finance, 3–53. 70

JERMANN, U. J. (1998): “Asset pricing in production economies,” Journal of Monetary Economics, 41,

257–275. 70

JOHANSEN, S. (1988): “Statistical analysis of cointegration vectors,” Journal of Economic Dynamics and

Control, 12, 231–254. 140, 141

154 BIBLIOGRAPHY

——— (1991): “Estimation and hypothesis testing of cointegration vectors in Gaussian vector auto-

regressive models,” Econometrica, 1551–1580. 140, 141

KAHN, C. AND A. WINTON (1998): “Ownership structure, speculation, and shareholder interven-

tion,” The Journal of Finance, 53, 99–129. 5

KANAGARETNAM, K., C. Y. LIM, AND G. J. LOBO (2014): “Effects of international institutional fac-

tors on earnings quality of banks,” Journal of Banking & Finance, 39, 87–106. 28, 29

KANDRAC, J. AND B. SCHLUSCHE (2017): “The Effect of Bank Supervision on Risk Taking: Evidence

from a Natural Experiment,” Finance and Economics Discussion Series 2017-079, Board of Gover-

nors of the Federal Reserve System. 5

KEMPF, E., A. MANCONI, AND O. SPALT (2016): “Distracted shareholders and corporate actions,”

The Review of Financial Studies, 30, 1660–1695. 5

KREPS, D. M. AND E. L. PORTEUS (1978): “Temporal resolution of uncertainty and dynamic choice

theory,” Econometrica, 185–200. 89

KUEHN, L.-A., N. PETROSKY-NADEAU, AND L. ZHANG (2012): “An equilibrium asset pricing mo-

del with labor market search,” Tech. rep., National Bureau of Economic Research. 70, 86

KUEHN, L.-A., M. SIMUTIN, AND J. J. WANG (2017): “A labor capital asset pricing model,” The

Journal of Finance, 72, 2131–2178. 70

LAEVEN, L. AND R. LEVINE (2007): “Is there a diversification discount in financial conglomerates?”

Journal of Financial Economics, 85, 331–367. 5, 14

LETTAU, M. AND S. LUDVIGSON (2001a): “Consumption, aggregate wealth, and expected stock

returns,” Journal of Finance, 815–849. 75

——— (2001b): “Resurrecting the (C) CAPM: A cross-sectional test when risk premia are time-

varying,” Journal of Political Economy, 109, 1238–1287. 70

LIU, L. X., T. M. WHITED, AND L. ZHANG (2009): “Investment-Based Expected Stock Returns,”

Journal of Political Economy, 117, 1105–1139. 86

BIBLIOGRAPHY 155

MAILATH, G. J., V. NOCKE, AND L. WHITE (2017): “When and How the Punishment Must Fit the

Crime,” International Economic Review, 58, 315–330. 38, 39, 41

MAUG, E. (1998): “Large shareholders as monitors: Is there a trade-off between liquidity and cont-

rol?” The Journal of Finance, 53, 65–98. 5

MCCONNELL, J. J. AND H. SERVAES (1990): “Additional evidence on equity ownership and corpo-

rate value,” Journal of Financial Economics, 27, 595–612. 5

MCCRARY, J. (2008): “Manipulation of the running variable in the regression discontinuity design:

A density test,” Journal of Econometrics, 142, 698–714. 3, 16, 18, 102

MERTON, R. C. (1977): “An analytic derivation of the cost of deposit insurance and loan guarantees:

An application of modern option pricing theory,” Journal of Banking & Finance, 1, 3–11. 5

MINTON, B. A., R. M. STULZ, AND A. G. TABOADA (2017): “Are larger banks valued more highly?”

Working Paper 23212, National Bureau of Economic Research. 14, 35

MORGAN, D. (2002): “Rating banks: Risk and uncertainty in an opaque industry,” The American

Economic Review, 92, 874–888. 5

NAKAMURA, E. AND J. STEINSSON (2011): “Price setting in forward-looking customer markets,”

Journal of Monetary Economics, 58, 220–233. 86

OSTROM, E., J. WALKER, AND R. GARDNER (1992): “Covenants with and without a Sword: Self-

governance Is Possible.” American Political Science Review, 86, 404–417. 42

PETROSKY-NADEAU, N. AND E. WASMER (2015): “Macroeconomic dynamics in a model of goods,

labor, and credit market frictions,” Journal of Monetary Economics, 72, 97–113. 70, 91

PETROSKY-NADEAU, N. AND L. ZHANG (2017): “Solving the Diamond–Mortensen–Pissarides mo-

del accurately,” Quantitative Economics, 8, 611–650. 92

PHILLIPS, P. C. AND S. OULIARIS (1990): “Asymptotic properties of residual based tests for cointe-

gration,” Econometrica, 165–193. 140

156 BIBLIOGRAPHY

RAHMAN, D. (2012): “But who will monitor the monitor?” The American Economic Review, 102, 2767–

2797. 42

SAUNDERS, A., E. STROCK, AND N. G. TRAVLOS (1990): “Ownership structure, deregulation, and

bank risk taking,” The Journal of Finance, 45, 643–654. 5

SAVOV, A. (2011): “Asset pricing with garbage,” The Journal of Finance, 66, 177–201. 70

SCHMIDT, C. AND R. FAHLENBRACH (2017): “Do exogenous changes in passive institutional ow-

nership affect corporate governance and firm value?” Journal of Financial Economics, 124, 285–306.

5

SHLEIFER, A. AND R. W. VISHNY (1986): “Large shareholders and corporate control,” Journal of

Political Economy, 94, 461–488. 4, 5, 30

STORESLETTEN, K., J.-V. R. RULL, AND Y. BAI (2011): “Demand Shocks that Look Like Productivity

Shocks,” in 2011 Meeting Papers, Society for Economic Dynamics, 99. 70

TOWNSEND, R. M. (1979): “Optimal contracts and competitive markets with costly state verifica-

tion,” Journal of Economic Theory, 21, 265–293. 2, 5, 7

VITORINO, M. A. (2014): “Understanding the Effect of Advertising on Stock Returns and Firm Value:

Theory and Evidence from a Structural Model,” Management Science, 60, 227–245. 70, 97

YELLEN, J. L. (2016): “Supervision and regulation,” Testimony Before the Committee on Financial

Services, U.S. House of Representatives, Washington, D.C. 2, 6

essays in financial economics - cmu

Documents